On Normalized Integral Table Algebras Fusion Rings

Download On Normalized Integral Table Algebras Fusion Rings full books in PDF, epub, and Kindle. Read online On Normalized Integral Table Algebras Fusion Rings ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

On Normalized Integral Table Algebras (Fusion Rings)

Author : Zvi Arad
Publisher : Springer Science & Business Media
ISBN 13 : 085729850X
Total Pages : 279 pages
Book Rating : 4.8/5 (572 download)

DOWNLOAD NOW!

Book Synopsis On Normalized Integral Table Algebras (Fusion Rings) by : Zvi Arad

Download or read book On Normalized Integral Table Algebras (Fusion Rings) written by Zvi Arad and published by Springer Science & Business Media. This book was released on 2011-07-20 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of table algebras was introduced in 1991 by Z. Arad and H. Blau in order to treat, in a uniform way, products of conjugacy classes and irreducible characters of finite groups. Today, table algebra theory is a well-established branch of modern algebra with various applications, including the representation theory of finite groups, algebraic combinatorics and fusion rules algebras. This book presents the latest developments in this area. Its main goal is to give a classification of the Normalized Integral Table Algebras (Fusion Rings) generated by a faithful non-real element of degree 3. Divided into 4 parts, the first gives an outline of the classification approach, while remaining parts separately treat special cases that appear during classification. A particularly unique contribution to the field, can be found in part four, whereby a number of the algebras are linked to the polynomial irreducible representations of the group SL3(C). This book will be of interest to research mathematicians and PhD students working in table algebras, group representation theory, algebraic combinatorics and integral fusion rule algebras.

Standard Integral Table Algebras Generated by a Non-real Element of Small Degree

Author : Zvi Arad
Publisher : Springer Science & Business Media
ISBN 13 : 3540428518
Total Pages : 129 pages
Book Rating : 4.5/5 (44 download)

DOWNLOAD NOW!

Book Synopsis Standard Integral Table Algebras Generated by a Non-real Element of Small Degree by : Zvi Arad

Download or read book Standard Integral Table Algebras Generated by a Non-real Element of Small Degree written by Zvi Arad and published by Springer Science & Business Media. This book was released on 2002-01-10 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is addressed to the researchers working in the theory of table algebras and association schemes. This area of algebraic combinatorics has been rapidly developed during the last decade. The volume contains further developments in the theory of table algebras. It collects several papers which deal with a classification problem for standard integral table algebras (SITA). More precisely, we consider SITA with a faithful non-real element of small degree. It turns out that such SITA with some extra conditions may be classified. This leads to new infinite series of SITA which has interesting properties. The last section of the book uses a part of obtained results in the classification of association schemes. This volume summarizes the research which was done at Bar-Ilan University in the academic year 1998/99.

On Standard Integral Table Algebras with Irreducible Elements of Small Degree

Author : Arisha Hag Ihia Hussam
Publisher :
ISBN 13 :
Total Pages : 628 pages
Book Rating : 4.:/5 (234 download)

DOWNLOAD NOW!

Book Synopsis On Standard Integral Table Algebras with Irreducible Elements of Small Degree by : Arisha Hag Ihia Hussam

Download or read book On Standard Integral Table Algebras with Irreducible Elements of Small Degree written by Arisha Hag Ihia Hussam and published by . This book was released on 1999 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fusion Rings with Degrees 1 and 4

Author : Tyler Lewis Mitchell
Publisher :
ISBN 13 : 9781339069623
Total Pages : 92 pages
Book Rating : 4.0/5 (696 download)

DOWNLOAD NOW!

Book Synopsis Fusion Rings with Degrees 1 and 4 by : Tyler Lewis Mitchell

Download or read book Fusion Rings with Degrees 1 and 4 written by Tyler Lewis Mitchell and published by . This book was released on 2015 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fusion rings are a class of table algebras that generalize group rings with basis the group and character rings of a finite group with basis the irreducible characters. Examples are the Grothendieck rings of fusion categories, algebraic structures that are related to conformal field theory. When considering the character ring of a group as a fusion ring, the usual degree of a character coincides with the value assigned by the degree map. Hence classifying fusion rings based on the degree set is a generalization of classifying groups based on the degrees of the irreducible characters. The main theorem classifies real fusion rings with degrees 1 and 4 such that all stabilizers have the same order (so-called stabilizer-regular fusion rings).

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 1884 pages
Book Rating : 4.X/5 (6 download)

DOWNLOAD NOW!

Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on Tensor Categories and Modular Functors

Author : Bojko Bakalov
Publisher : American Mathematical Soc.
ISBN 13 : 0821826867
Total Pages : 232 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Lectures on Tensor Categories and Modular Functors by : Bojko Bakalov

Download or read book Lectures on Tensor Categories and Modular Functors written by Bojko Bakalov and published by American Mathematical Soc.. This book was released on 2001 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and Moore-Seiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill. The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advanced-graduate level.

Tensor Categories

Author : Pavel Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 1470434415
Total Pages : 362 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis Tensor Categories by : Pavel Etingof

Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.

Fusion Systems in Algebra and Topology

Author : Michael Aschbacher
Publisher : Cambridge University Press
ISBN 13 : 1107601002
Total Pages : 329 pages
Book Rating : 4.1/5 (76 download)

DOWNLOAD NOW!

Book Synopsis Fusion Systems in Algebra and Topology by : Michael Aschbacher

Download or read book Fusion Systems in Algebra and Topology written by Michael Aschbacher and published by Cambridge University Press. This book was released on 2011-08-25 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.

Mathematics for Machine Learning

Author : Marc Peter Deisenroth
Publisher : Cambridge University Press
ISBN 13 : 1108569323
Total Pages : 392 pages
Book Rating : 4.1/5 (85 download)

DOWNLOAD NOW!

Book Synopsis Mathematics for Machine Learning by : Marc Peter Deisenroth

Download or read book Mathematics for Machine Learning written by Marc Peter Deisenroth and published by Cambridge University Press. This book was released on 2020-04-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

The Nuclear Many-Body Problem

Author : Peter Ring
Publisher : Springer Science & Business Media
ISBN 13 : 9783540212065
Total Pages : 742 pages
Book Rating : 4.2/5 (12 download)

DOWNLOAD NOW!

Book Synopsis The Nuclear Many-Body Problem by : Peter Ring

Download or read book The Nuclear Many-Body Problem written by Peter Ring and published by Springer Science & Business Media. This book was released on 2004-03-25 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: Study Edition

Combinatorial Commutative Algebra

Author : Ezra Miller
Publisher : Springer Science & Business Media
ISBN 13 : 9780387237077
Total Pages : 442 pages
Book Rating : 4.2/5 (37 download)

DOWNLOAD NOW!

Book Synopsis Combinatorial Commutative Algebra by : Ezra Miller

Download or read book Combinatorial Commutative Algebra written by Ezra Miller and published by Springer Science & Business Media. This book was released on 2005-06-21 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Modular Forms, a Computational Approach

Author : William A. Stein
Publisher : American Mathematical Soc.
ISBN 13 : 0821839608
Total Pages : 290 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Modular Forms, a Computational Approach by : William A. Stein

Download or read book Modular Forms, a Computational Approach written by William A. Stein and published by American Mathematical Soc.. This book was released on 2007-02-13 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.

Semisolvability of Semisimple Hopf Algebras of Low Dimension

Author : Sonia Natale
Publisher : American Mathematical Soc.
ISBN 13 : 0821839489
Total Pages : 138 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Semisolvability of Semisimple Hopf Algebras of Low Dimension by : Sonia Natale

Download or read book Semisolvability of Semisimple Hopf Algebras of Low Dimension written by Sonia Natale and published by American Mathematical Soc.. This book was released on 2007 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author proves that every semisimple Hopf algebra of dimension less than $60$ over an algebraically closed field $k$ of characteristic zero is either upper or lower semisolvable up to a cocycle twist.

Chebyshev and Fourier Spectral Methods

Author : John P. Boyd
Publisher : Courier Corporation
ISBN 13 : 0486411834
Total Pages : 690 pages
Book Rating : 4.4/5 (864 download)

DOWNLOAD NOW!

Book Synopsis Chebyshev and Fourier Spectral Methods by : John P. Boyd

Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2001-12-03 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.

Noncommutative Localization in Algebra and Topology

Author : Andrew Ranicki
Publisher : Cambridge University Press
ISBN 13 : 9780521681605
Total Pages : 332 pages
Book Rating : 4.6/5 (816 download)

DOWNLOAD NOW!

Book Synopsis Noncommutative Localization in Algebra and Topology by : Andrew Ranicki

Download or read book Noncommutative Localization in Algebra and Topology written by Andrew Ranicki and published by Cambridge University Press. This book was released on 2006-02-09 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

DOWNLOAD NOW!

Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Modular Representation Theory

Author : D. Benson
Publisher : Springer Science & Business Media
ISBN 13 : 3540133895
Total Pages : 246 pages
Book Rating : 4.5/5 (41 download)

DOWNLOAD NOW!

Book Synopsis Modular Representation Theory by : D. Benson

Download or read book Modular Representation Theory written by D. Benson and published by Springer Science & Business Media. This book was released on 1984 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reprint of a 1983 Yale graduate course makes results in modular representation theory accessible to an audience ranging from second-year graduate students to established mathematicians. Following a review of background material, the lectures examine three closely connected topics in modular representation theory of finite groups: representations rings; almost split sequences and the Auslander-Reiten quiver; and complexity and cohomology varieties, which has become a major theme in representation theory.