Examples Of Algebras Of Small Gelfand Kirillov Dimension

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Growth of Algebras and Gelfand-Kirillov Dimension

Author : G. R. Krause
Publisher : American Mathematical Soc.
ISBN 13 : 0821808591
Total Pages : 224 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Growth of Algebras and Gelfand-Kirillov Dimension by : G. R. Krause

Download or read book Growth of Algebras and Gelfand-Kirillov Dimension written by G. R. Krause and published by American Mathematical Soc.. This book was released on 2000 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the two decades that preceded the publication of the first edition of this book, the Gelfand-Kirillov dimension had emerged as a very useful and powerful tool for investigating non-commutative algebras. At that time, the basic ideas and results were scattered throughout various journal articles. The first edition of this book provided a much-needed reliable and coherent single source of information. Since that time, the book has become the standard reference source for researchers. For this edition, the authors incorporated the original text with only minor modifications. Errors have been corrected, items have been rephrased, and more mathematical expressions have been displayed for the purpose of clarity. The newly added Chapter 12 provides broad overviews of the new developments that have surfaced in the last few years, with references to the literature for details. The bibliography has been updated and accordingly, almost double the size of the original one. The faithful revision and contemporary design of this work offers time-honored expertise with modern functionality. A keenly appealing combination. So, whether for the classroom, the well-tended mathematical books collection, or the research desk, this book holds unprecedented relevance.

Commutative Algebra and Noncommutative Algebraic Geometry

Author : David Eisenbud
Publisher : Cambridge University Press
ISBN 13 : 1107065623
Total Pages : 463 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Commutative Algebra and Noncommutative Algebraic Geometry by : David Eisenbud

Download or read book Commutative Algebra and Noncommutative Algebraic Geometry written by David Eisenbud and published by Cambridge University Press. This book was released on 2015-11-19 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.

New Trends in Noncommutative Algebra

Author : Ara, Pere
Publisher : American Mathematical Soc.
ISBN 13 : 0821852973
Total Pages : 326 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis New Trends in Noncommutative Algebra by : Ara, Pere

Download or read book New Trends in Noncommutative Algebra written by Ara, Pere and published by American Mathematical Soc.. This book was released on 2012 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference `New Trends in Noncommutative Algebra', held at the University of Washington, Seattle, in August 2010. The articles will provide researchers and graduate students with an indispensable overview of topics of current interest. Specific fields covered include: noncommutative algebraic geometry, representation theory, Calabi-Yau algebras, quantum algebras and deformation quantization, Poisson algebras, group algebras, and noncommutative Iwasawa algebras.

Categorical, Homological and Combinatorial Methods in Algebra

Author : Ashish K. Srivastava
Publisher : American Mathematical Soc.
ISBN 13 : 1470443686
Total Pages : 370 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Categorical, Homological and Combinatorial Methods in Algebra by : Ashish K. Srivastava

Download or read book Categorical, Homological and Combinatorial Methods in Algebra written by Ashish K. Srivastava and published by American Mathematical Soc.. This book was released on 2020-06-23 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the AMS Special Session, in honor of S. K. Jain's 80th birthday, on Categorical, Homological and Combinatorial Methods in Algebra held from March 16–18, 2018, at Ohio State University, Columbus, Ohio. The articles contained in this volume aim to showcase the current state of art in categorical, homological and combinatorial aspects of algebra.

Computational Aspects of Polynomial Identities

Author : Alexei Kanel-Belov
Publisher : CRC Press
ISBN 13 : 1498720099
Total Pages : 436 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Computational Aspects of Polynomial Identities by : Alexei Kanel-Belov

Download or read book Computational Aspects of Polynomial Identities written by Alexei Kanel-Belov and published by CRC Press. This book was released on 2015-10-22 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Aspects of Polynomial Identities: Volume l, Kemer's Theorems, 2nd Edition presents the underlying ideas in recent polynomial identity (PI)-theory and demonstrates the validity of the proofs of PI-theorems. This edition gives all the details involved in Kemer's proof of Specht's conjecture for affine PI-algebras in characteristic 0.The

Ring Theory V2

Author :
Publisher : Academic Press
ISBN 13 : 0080874479
Total Pages : 477 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Ring Theory V2 by :

Download or read book Ring Theory V2 written by and published by Academic Press. This book was released on 1988-07-01 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ring Theory V2

Hopf Algebras and Root Systems

Author : István Heckenberger
Publisher : American Mathematical Soc.
ISBN 13 : 1470452324
Total Pages : 606 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hopf Algebras and Root Systems by : István Heckenberger

Download or read book Hopf Algebras and Root Systems written by István Heckenberger and published by American Mathematical Soc.. This book was released on 2020-06-19 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal of the book is to present from scratch and with complete proofs the theory of Nichols algebras (or quantum symmetric algebras) and the surprising relationship between Nichols algebras and generalized root systems. In general, Nichols algebras are not classified by Cartan graphs and their root systems. However, extending partial results in the literature, the authors were able to associate a Cartan graph to a large class of Nichols algebras. This allows them to determine the structure of right coideal subalgebras of Nichols systems which generalize Nichols algebras. As applications of these results, the book contains a classification of right coideal subalgebras of quantum groups and of the small quantum groups, and a proof of the existence of PBW-bases that does not involve case by case considerations. The authors also include short chapter summaries at the beginning of each chapter and historical notes at the end of each chapter. The theory of Cartan graphs, Weyl groupoids, and generalized root systems appears here for the first time in a book form. Hence, the book serves as an introduction to the modern classification theory of pointed Hopf algebras for advanced graduate students and researchers working in categorial aspects and classification theory of Hopf algebras and their generalization.

Recent Advances in Noncommutative Algebra and Geometry

Author : K. A. Brown
Publisher : American Mathematical Society
ISBN 13 : 1470472392
Total Pages : 288 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Recent Advances in Noncommutative Algebra and Geometry by : K. A. Brown

Download or read book Recent Advances in Noncommutative Algebra and Geometry written by K. A. Brown and published by American Mathematical Society. This book was released on 2024-05-30 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry, held from June 20–24, 2022, at the University of Washington, Seattle, in honor of S. Paul Smith's 65th birthday. The articles reflect the wide interests of Smith and provide researchers and graduate students with an indispensable overview of topics of current interest. Specific fields covered include: noncommutative algebraic geometry, representation theory, Hopf algebras and quantum groups, the elliptic algebras of Feigin and Odesskii, Calabi-Yau algebras, Artin-Schelter regular algebras, deformation theory, and Lie theory. In addition to original research contributions the volume includes an introductory essay reviewing Smith's research contributions in these fields, and several survey articles.

Methods in Ring Theory

Author : Vesselin Drensky
Publisher : CRC Press
ISBN 13 : 9780824701833
Total Pages : 332 pages
Book Rating : 4.7/5 (18 download)

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Book Synopsis Methods in Ring Theory by : Vesselin Drensky

Download or read book Methods in Ring Theory written by Vesselin Drensky and published by CRC Press. This book was released on 1998-03-27 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Furnishes important research papers and results on group algebras and PI-algebras presented recently at the Conference on Methods in Ring Theory held in Levico Terme, Italy-familiarizing researchers with the latest topics, techniques, and methodologies encompassing contemporary algebra."

Algebraists' Homage: Papers in Ring Theory and Related Topics

Author : Shimshon A. Amitsur
Publisher : American Mathematical Soc.
ISBN 13 : 082185013X
Total Pages : 420 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraists' Homage: Papers in Ring Theory and Related Topics by : Shimshon A. Amitsur

Download or read book Algebraists' Homage: Papers in Ring Theory and Related Topics written by Shimshon A. Amitsur and published by American Mathematical Soc.. This book was released on 1982 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Semigroup Algebras

Author : Jan Okninski
Publisher : CRC Press
ISBN 13 : 1000147665
Total Pages : 319 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Semigroup Algebras by : Jan Okninski

Download or read book Semigroup Algebras written by Jan Okninski and published by CRC Press. This book was released on 2020-08-27 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gathers and unifies the results of the theory of noncommutative semigroup rings, primarily drawing on the literature of the last 10 years, and including several new results. Okninski (Warsaw U., Poland) restricts coverage to the ring theoretical properties for which a systematic treatment is current

Dimensions of Ring Theory

Author : C. Nastasescu
Publisher : Springer Science & Business Media
ISBN 13 : 9400938357
Total Pages : 369 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Dimensions of Ring Theory by : C. Nastasescu

Download or read book Dimensions of Ring Theory written by C. Nastasescu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Gad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of s9phistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Lie Theory and Its Applications in Physics

Author : Vladimir Dobrev
Publisher : Springer Nature
ISBN 13 : 9811947511
Total Pages : 526 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Lie Theory and Its Applications in Physics by : Vladimir Dobrev

Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer Nature. This book was released on 2023-01-29 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions to the Workshop "Lie Theory and Its Applications in Physics" held in Sofia, Bulgaria (on-line) in June 2021. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a big interdisciplinary and interrelated field. The topics covered in this Volume are the most modern trends in the field of the Workshop: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, Exceptional quantum algebra for the standard model of particle physics, Gauge Theories and Applications, Structures on Lie Groups and Lie Algebras. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Group Theory, Statistics, and Cryptography

Author : Alexei G. Myasnikov
Publisher : American Mathematical Soc.
ISBN 13 : 0821834444
Total Pages : 186 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Group Theory, Statistics, and Cryptography by : Alexei G. Myasnikov

Download or read book Group Theory, Statistics, and Cryptography written by Alexei G. Myasnikov and published by American Mathematical Soc.. This book was released on 2004 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of contributions by speakers at the AMS Special Session on Combinatorial and Statistical Group Theory held at New York University. Readers will find a variety of contributions, including survey papers on applications of group theory in cryptography, research papers on various aspects of statistical group theory, and papers on more traditional combinatorial group theory. The book is suitable for graduate students and research mathematicians interested in group theory and its applications to cryptography.

An Introduction to Lie Groups and Lie Algebras

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
ISBN 13 : 0521889693
Total Pages : 237 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov

Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.

Quantum Groups and Their Primitive Ideals

Author : Anthony Joseph
Publisher : Springer Science & Business Media
ISBN 13 : 3642784003
Total Pages : 394 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Quantum Groups and Their Primitive Ideals by : Anthony Joseph

Download or read book Quantum Groups and Their Primitive Ideals written by Anthony Joseph and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: by a more general quadratic algebra (possibly obtained by deformation) and then to derive Rq [G] by requiring it to possess the latter as a comodule. A third principle is to focus attention on the tensor structure of the cat egory of (!; modules. This means of course just defining an algebra structure on Rq[G]; but this is to be done in a very specific manner. Concretely the category is required to be braided and this forces (9.4.2) the existence of an "R-matrix" satisfying in particular the quantum Yang-Baxter equation and from which the algebra structure of Rq[G] can be written down (9.4.5). Finally there was a search for a perfectly self-dual model for Rq[G] which would then be isomorphic to Uq(g). Apparently this failed; but V. G. Drinfeld found that it could be essentially made to work for the "Borel part" of Uq(g) denoted U (b) and further found a general construction (the Drinfeld double) q mirroring a Lie bialgebra. This gives Uq(g) up to passage to a quotient. One of the most remarkable aspects of the above superficially different ap proaches is their extraordinary intercoherence. In particular they essentially all lead for G semisimple to the same and hence "canonical", objects Rq[G] and Uq(g), though this epithet may as yet be premature.

Combinatorial Algebra: Syntax and Semantics

Author : Mark V. Sapir
Publisher : Springer
ISBN 13 : 3319080318
Total Pages : 369 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Combinatorial Algebra: Syntax and Semantics by : Mark V. Sapir

Download or read book Combinatorial Algebra: Syntax and Semantics written by Mark V. Sapir and published by Springer. This book was released on 2014-10-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Algebra: Syntax and Semantics provides comprehensive account of many areas of combinatorial algebra. It contains self-contained proofs of more than 20 fundamental results, both classical and modern. This includes Golod–Shafarevich and Olshanskii's solutions of Burnside problems, Shirshov's solution of Kurosh's problem for PI rings, Belov's solution of Specht's problem for varieties of rings, Grigorchuk's solution of Milnor's problem, Bass–Guivarc'h theorem about growth of nilpotent groups, Kleiman's solution of Hanna Neumann's problem for varieties of groups, Adian's solution of von Neumann-Day's problem, Trahtman's solution of the road coloring problem of Adler, Goodwyn and Weiss. The book emphasize several ``universal" tools, such as trees, subshifts, uniformly recurrent words, diagrams and automata. With over 350 exercises at various levels of difficulty and with hints for the more difficult problems, this book can be used as a textbook, and aims to reach a wide and diversified audience. No prerequisites beyond standard courses in linear and abstract algebra are required. The broad appeal of this textbook extends to a variety of student levels: from advanced high-schoolers to undergraduates and graduate students, including those in search of a Ph.D. thesis who will benefit from the “Further reading and open problems” sections at the end of Chapters 2 –5. The book can also be used for self-study, engaging those beyond t he classroom setting: researchers, instructors, students, virtually anyone who wishes to learn and better understand this important area of mathematics.