Lectures On Algebraic Categorification

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Lectures on Algebraic Categorification

Author : Volodymyr Mazorchuk
Publisher : European Mathematical Society
ISBN 13 : 9783037191088
Total Pages : 136 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Lectures on Algebraic Categorification by : Volodymyr Mazorchuk

Download or read book Lectures on Algebraic Categorification written by Volodymyr Mazorchuk and published by European Mathematical Society. This book was released on 2012 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term ``categorification'' was introduced by Louis Crane in 1995 and refers to the process of replacing set-theoretic notions by the corresponding category-theoretic analogues. This text mostly concentrates on algebraical aspects of the theory, presented in the historical perspective, but also contains several topological applications, in particular, an algebraic (or, more precisely, representation-theoretical) approach to categorification. It consists of fifteen sections corresponding to fifteen one-hour lectures given during a Master Class at Aarhus University, Denmark in October 2010. There are some exercises collected at the end of the text and a rather extensive list of references. Video recordings of all (but one) lectures are available from the Master Class website. The book provides an introductory overview of the subject rather than a fully detailed monograph. The emphasis is made on definitions, examples and formulations of the results. Most proofs are either briefly outlined or omitted. However, complete proofs can be found by tracking references. It is assumed that the reader is familiar with the basics of category theory, representation theory, topology, and Lie algebra.

Lectures On Sl_2(c)-modules

Author : Mazorchuk Volodymyr
Publisher : World Scientific Publishing Company
ISBN 13 : 1911299441
Total Pages : 276 pages
Book Rating : 4.9/5 (112 download)

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Book Synopsis Lectures On Sl_2(c)-modules by : Mazorchuk Volodymyr

Download or read book Lectures On Sl_2(c)-modules written by Mazorchuk Volodymyr and published by World Scientific Publishing Company. This book was released on 2009-12-04 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is directed primarily at undergraduate and postgraduate students interested to get acquainted with the representation theory of Lie algebras. The book treats the case of the smallest simple Lie algebra, namely, the Lie algebra sl_2. It contains classical contents including the description of all finite-dimensional modules and an introduction to the universal enveloping algebras with its primitive ideals, alongside non-classical contents including the description of all simple weight modules, the category of all weight modules, a detailed description of the category O, and especially, a description of all simple modules. The book also contains an account of a new research direction: the categorification of simple finite-dimensional modules./a

Representations and Nilpotent Orbits of Lie Algebraic Systems

Author : Maria Gorelik
Publisher : Springer Nature
ISBN 13 : 3030235319
Total Pages : 553 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Representations and Nilpotent Orbits of Lie Algebraic Systems by : Maria Gorelik

Download or read book Representations and Nilpotent Orbits of Lie Algebraic Systems written by Maria Gorelik and published by Springer Nature. This book was released on 2019-10-18 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.

Forty Years Of Algebraic Groups, Algebraic Geometry, And Representation Theory In China: In Memory Of The Centenary Year Of Xihua Cao's Birth

Download Forty Years Of Algebraic Groups, Algebraic Geometry, And Representation Theory In China: In Memory Of The Centenary Year Of Xihua Cao's Birth PDF Online Free

Author : Jie Du
Publisher : World Scientific
ISBN 13 : 9811263507
Total Pages : 490 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Forty Years Of Algebraic Groups, Algebraic Geometry, And Representation Theory In China: In Memory Of The Centenary Year Of Xihua Cao's Birth by : Jie Du

Download or read book Forty Years Of Algebraic Groups, Algebraic Geometry, And Representation Theory In China: In Memory Of The Centenary Year Of Xihua Cao's Birth written by Jie Du and published by World Scientific. This book was released on 2022-10-21 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Xihua Cao (1920-2005) was a leading scholar at East China Normal University (ECNU) and a famous algebraist in China. His contribution to the Chinese academic circle is particularly the formation of a world-renowned 'ECNU School' in algebra, covering research areas include algebraic groups, quantum groups, algebraic geometry, Lie algebra, algebraic number theory, representation theory and other hot fields. In January 2020, in order to commemorate Professor Xihua Cao's centenary birthday, East China Normal University held a three-day academic conference. Scholars at home and abroad gave dedications or delivered lectures in the conference. This volume originates from the memorial conference, collecting the dedications of scholars, reminiscences of family members, and 16 academic articles written based on the lectures in the conference, covering a wide range of research hot topics in algebra. The book shows not only scholars' respect and memory for Professor Xihua Cao, but also the research achievements of Chinese scholars at home and abroad.

Encyclopedia of Knot Theory

Author : Colin Adams
Publisher : CRC Press
ISBN 13 : 1000222381
Total Pages : 954 pages
Book Rating : 4.0/5 (2 download)

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Book Synopsis Encyclopedia of Knot Theory by : Colin Adams

Download or read book Encyclopedia of Knot Theory written by Colin Adams and published by CRC Press. This book was released on 2021-02-10 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory

Buildings, Finite Geometries and Groups

Author : N.S. Narasimha Sastry
Publisher : Springer Science & Business Media
ISBN 13 : 1461407095
Total Pages : 348 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Buildings, Finite Geometries and Groups by : N.S. Narasimha Sastry

Download or read book Buildings, Finite Geometries and Groups written by N.S. Narasimha Sastry and published by Springer Science & Business Media. This book was released on 2011-11-13 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the Proceedings of the ICM 2010 Satellite Conference on “Buildings, Finite Geometries and Groups” organized at the Indian Statistical Institute, Bangalore, during August 29 – 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, etc. These articles reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective the authors bring in their articles on the current developments and the major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these areas.

When Form Becomes Substance

Author : Luciano Boi
Publisher : Springer Nature
ISBN 13 : 3030831256
Total Pages : 607 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis When Form Becomes Substance by : Luciano Boi

Download or read book When Form Becomes Substance written by Luciano Boi and published by Springer Nature. This book was released on 2022-11-30 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This interdisciplinary volume collects contributions from experts in their respective fields with as common theme diagrams. Diagrams play a fundamental role in the mathematical visualization and philosophical analysis of forms in space. Some of the most interesting and profound recent developments in contemporary sciences, whether in topology, geometry, dynamic systems theory, quantum field theory or string theory, have been made possible by the introduction of new types of diagrams, which, in addition to their essential role in the discovery of new classes of spaces and phenomena, have contributed to enriching and clarifying the meaning of the operations, structures and properties that are at the heart of these spaces and phenomena. The volume gives a closer look at the scope and the nature of diagrams as constituents of mathematical and physical thought, their function in contemporary artistic work, and appraise, in particular, the actual importance of the diagrams of knots, of braids, of fields, of interaction, of strings in topology and geometry, in quantum physics and in cosmology, but also in theory of perception, in plastic arts and in philosophy. The editors carefully curated this volume to be an inspiration to students and researchers in philosophy, phenomenology, mathematics and the sciences, as well as artists, musicians and the general interested audience.

Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification

Author : Jacob Greenstein
Publisher : Springer Nature
ISBN 13 : 3030638499
Total Pages : 453 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification by : Jacob Greenstein

Download or read book Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification written by Jacob Greenstein and published by Springer Nature. This book was released on 2022-03-11 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.

Dynamics: Topology and Numbers

Author : Pieter Moree
Publisher : American Mathematical Soc.
ISBN 13 : 147045100X
Total Pages : 347 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Dynamics: Topology and Numbers by : Pieter Moree

Download or read book Dynamics: Topology and Numbers written by Pieter Moree and published by American Mathematical Soc.. This book was released on 2020-02-12 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.

Lectures on Fundamental Concepts of Algebra and Geometry

Author : John Wesley Young
Publisher : Merchant Books
ISBN 13 : 9781603861175
Total Pages : 252 pages
Book Rating : 4.8/5 (611 download)

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Book Synopsis Lectures on Fundamental Concepts of Algebra and Geometry by : John Wesley Young

Download or read book Lectures on Fundamental Concepts of Algebra and Geometry written by John Wesley Young and published by Merchant Books. This book was released on 2008-06-01 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: An unabridged printing, with text and all figures digitally enlarged: Euclid's Elements - A Non-Euclidean World - On The History Of The Parallel Postulate - Logical Significance Of Definitions, Axioms, And Postulates - Consistency, Independence, And Categoricalness Of A Set Of Assumptions - Class, Correspondence. Number - Order, Discrete Sequences - The Sequence Of Cardinal Numbers, Denumerable Classes, Dense Classes, Continuous Classes - Group, Number System - Historical And Logical Development Of The Concept Of Real Number - Negative Numbers - Ordinary And Higher Complex Numbers - Geometry. Hilbert's Assumptions - Hilbert's Assumptions Continued - Pieri's Assumptions - The Dimensions Of A Class - Spaces Of Four Or More Dimensions - Algebra And Geometry - Variable And Function - Limit - General Conclusions - The Growth Of Algebraic Symbolism by U. G. Mitchell

Lectures on Sl_2(c)-modules

Author :
Publisher : World Scientific
ISBN 13 : 1848165196
Total Pages : 274 pages
Book Rating : 4.8/5 (481 download)

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Book Synopsis Lectures on Sl_2(c)-modules by :

Download or read book Lectures on Sl_2(c)-modules written by and published by World Scientific. This book was released on 2009 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures in Abstract Algebra

Author : Nathan Jacobson
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (72 download)

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Book Synopsis Lectures in Abstract Algebra by : Nathan Jacobson

Download or read book Lectures in Abstract Algebra written by Nathan Jacobson and published by . This book was released on 1953 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introductory Lectures on Knot Theory

Author : Louis H. Kauffman
Publisher : World Scientific
ISBN 13 : 9814313009
Total Pages : 577 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Introductory Lectures on Knot Theory by : Louis H. Kauffman

Download or read book Introductory Lectures on Knot Theory written by Louis H. Kauffman and published by World Scientific. This book was released on 2012 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.

Lectures in Knot Theory

Author : Józef H. Przytycki
Publisher : Springer Nature
ISBN 13 : 3031400445
Total Pages : 525 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Lectures in Knot Theory by : Józef H. Przytycki

Download or read book Lectures in Knot Theory written by Józef H. Przytycki and published by Springer Nature. This book was released on with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on Algebraic Groups

Author : Jacques Tits
Publisher :
ISBN 13 :
Total Pages : 336 pages
Book Rating : 4.:/5 (19 download)

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Book Synopsis Lectures on Algebraic Groups by : Jacques Tits

Download or read book Lectures on Algebraic Groups written by Jacques Tits and published by . This book was released on 1967 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Categorification in Geometry, Topology, and Physics

Author : Anna Beliakova
Publisher : American Mathematical Soc.
ISBN 13 : 1470428210
Total Pages : 282 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Categorification in Geometry, Topology, and Physics by : Anna Beliakova

Download or read book Categorification in Geometry, Topology, and Physics written by Anna Beliakova and published by American Mathematical Soc.. This book was released on 2017-02-21 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorification is a powerful tool for relating various branches of mathematics and exploiting the commonalities between fields. It provides a language emphasizing essential features and allowing precise relationships between vastly different fields. This volume focuses on the role categorification plays in geometry, topology, and physics. These articles illustrate many important trends for the field including geometric representation theory, homotopical methods in link homology, interactions between higher representation theory and gauge theory, and double affine Hecke algebra approaches to link homology. The companion volume (Contemporary Mathematics, Volume 683) is devoted to categorification and higher representation theory.

Low Dimensional Topology

Author : Tomasz Mrowka
Publisher : American Mathematical Soc.
ISBN 13 : 0821886967
Total Pages : 331 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Low Dimensional Topology by : Tomasz Mrowka

Download or read book Low Dimensional Topology written by Tomasz Mrowka and published by American Mathematical Soc.. This book was released on 2009-01-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low-dimensional topology has long been a fertile area for the interaction of many different disciplines of mathematics, including differential geometry, hyperbolic geometry, combinatorics, representation theory, global analysis, classical mechanics, and theoretical physics. The Park City Mathematics Institute summer school in 2006 explored in depth the most exciting recent aspects of this interaction, aimed at a broad audience of both graduate students and researchers. The present volume is based on lectures presented at the summer school on low-dimensional topology. These notes give fresh, concise, and high-level introductions to these developments, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field of low-dimensional topology and to senior researchers wishing to keep up with current developments. The volume begins with notes based on a special lecture by John Milnor about the history of the topology of manifolds. It also contains notes from lectures by Cameron Gordon on the basics of three-manifold topology and surgery problems, Mikhail Khovanov on his homological invariants for knots, John Etnyre on contact geometry, Ron Fintushel and Ron Stern on constructions of exotic four-manifolds, David Gabai on the hyperbolic geometry and the ending lamination theorem, Zoltan Szabo on Heegaard Floer homology for knots and three manifolds, and John Morgan on Hamilton's and Perelman's work on Ricci flow and geometrization.