Polynomial Identities of Algebras in Positive Characteristic
Author: Sérgio Mota Alves
Publisher:
Published: 2005
Total Pages: 26
ISBN-13:
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Polynomial Identities in Algebras
Author: Onofrio Mario Di Vincenzo
Publisher: Springer Nature
Published: 2021-03-22
Total Pages: 421
ISBN-13: 3030631117
DOWNLOAD EBOOKThis volume contains the talks given at the INDAM workshop entitled "Polynomial identites in algebras", held in Rome in September 2019. The purpose of the book is to present the current state of the art in the theory of PI-algebras. The review of the classical results in the last few years has pointed out new perspectives for the development of the theory. In particular, the contributions emphasize on the computational and combinatorial aspects of the theory, its connection with invariant theory, representation theory, growth problems. It is addressed to researchers in the field.
Identities of Algebras and their Representations
Author: I︠U︡riĭ Pitrimovich Razmyslov
Publisher: American Mathematical Soc.
Published: 1994
Total Pages: 468
ISBN-13: 9780821846087
DOWNLOAD EBOOKDuring the past forty years, a new trend in the theory of associative algebras, Lie algebras, and their representations has formed under the influence of mathematical logic and universal algebra, namely, the theory of varieties and identities of associative algebras, Lie algebras, and their representations. The last twenty years have seen the creation of the method of 2-words and *a-functions, which allowed a number of problems in the theory of groups, rings, Lie algebras, and their representations to be solved in a unified way. The possibilities of this method are far from exhausted. This book sums up the applications of the method of 2-words and *a-functions in the theory of varieties and gives a systematic exposition of contemporary achievements in the theory of identities of algebras and their representations closely related to this method. The aim is to make these topics accessible to a wider group of mathematicians.
RINGS WITH POLYNOMIAL IDENTITIES AND FINITE DIMENSIONAL REPRESENTATIONS OF Algebras
Author: Eli Aljadeff
Publisher:
Published: 2020
Total Pages:
ISBN-13: 9781470456955
DOWNLOAD EBOOKPolynomial Identities And Combinatorial Methods
Author: Antonio Giambruno
Publisher: CRC Press
Published: 2003-05-20
Total Pages: 442
ISBN-13: 9780203911549
DOWNLOAD EBOOKPolynomial Identities and Combinatorial Methods presents a wide range of perspectives on topics ranging from ring theory and combinatorics to invariant theory and associative algebras. It covers recent breakthroughs and strategies impacting research on polynomial identities and identifies new concepts in algebraic combinatorics, invariant and representation theory, and Lie algebras and superalgebras for novel studies in the field. It presents intensive discussions on various methods and techniques relating the theory of polynomial identities to other branches of algebraic study and includes discussions on Hopf algebras and quantum polynomials, free algebras and Scheier varieties.
Rings with Polynomial Identities
Author: Claudio Procesi
Publisher:
Published: 1973
Total Pages: 232
ISBN-13:
DOWNLOAD EBOOKIntroduction to Representation Theory
Author: Pavel I. Etingof
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 240
ISBN-13: 0821853511
DOWNLOAD EBOOKVery roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Algebras and Representation Theory
Author: Karin Erdmann
Publisher: Springer
Published: 2018-09-07
Total Pages: 304
ISBN-13: 3319919989
DOWNLOAD EBOOKThis carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.
Computational Aspects of Polynomial Identities
Author: Alexei Kanel-Belov
Publisher: CRC Press
Published: 2005-02-22
Total Pages: 400
ISBN-13: 1439863725
DOWNLOAD EBOOKA comprehensive study of the main research done in polynomial identities over the last 25 years, including Kemer's solution to the Specht problem in characteristic O and examples in the characteristic p situation. The authors also cover codimension theory, starting with Regev's theorem and continuing through the Giambruno-Zaicev exponential rank. T
Rings with Polynomial Identities and Finite Dimensional Representations of Algebras
Author: Eli Aljadeff
Publisher: American Mathematical Soc.
Published: 2020-12-14
Total Pages: 630
ISBN-13: 1470451743
DOWNLOAD EBOOKA polynomial identity for an algebra (or a ring) A A is a polynomial in noncommutative variables that vanishes under any evaluation in A A. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley–Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem.
