Polynomial Identities in Algebras PDF Download
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Author: Onofrio Mario Di Vincenzo
Publisher: Springer Nature
ISBN: 3030631117
Category : Mathematics
Languages : en
Pages : 421
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Book Description
This 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.
Author: Onofrio Mario Di Vincenzo
Publisher: Springer Nature
ISBN: 3030631117
Category : Mathematics
Languages : en
Pages : 421
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Book Description
This 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.
Author: Antonio Giambruno
Publisher: CRC Press
ISBN: 9780203911549
Category : Mathematics
Languages : en
Pages : 442
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Book Description
Polynomial 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.
Author: A. Giambruno
Publisher: American Mathematical Soc.
ISBN: 0821838296
Category : Mathematics
Languages : en
Pages : 370
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Book Description
This book gives a state of the art approach to the study of polynomial identities satisfied by a given algebra by combining methods of ring theory, combinatorics, and representation theory of groups with analysis. The idea of applying analytical methods to the theory of polynomial identities appeared in the early 1970s and this approach has become one of the most powerful tools of the theory. A PI-algebra is any algebra satisfying at least one nontrivial polynomial identity. This includes the polynomial rings in one or several variables, the Grassmann algebra, finite-dimensional algebras, and many other algebras occurring naturally in mathematics. The core of the book is the proof that the sequence of co-dimensions of any PI-algebra has integral exponential growth - the PI-exponent of the algebra. Later chapters further apply these results to subjects such as a characterization of varieties of algebras having polynomial growth and a classification of varieties that are minimal for a given exponent.
Author: Vesselin Drensky
Publisher: Birkhäuser
ISBN: 3034879342
Category : Mathematics
Languages : en
Pages : 197
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Book Description
These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The greater part of recent research in polynomial identity rings is about combinatorial questions, and the combinatorial part of the lecture notes gives an up-to-date account of recent research. On the other hand, the main structural results have been known for some time, and the emphasis there is on a presentation accessible to newcomers to the subject.
Author: Eli Aljadeff
Publisher:
ISBN: 9781470456955
Category : PI-algebras
Languages : en
Pages :
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Book Description
Author: Claudio Procesi
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 232
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Book Description
Author: Paul A. Fuhrmann
Publisher: Springer Science & Business Media
ISBN: 1441987347
Category : Mathematics
Languages : en
Pages : 368
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Book Description
A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great theoretical interest, but lead to computational algorithms. Quadratic forms are treated from the same perspective, with emphasis on the important examples of Bezoutian and Hankel forms. These topics are of great importance in applied areas such as signal processing, numerical linear algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra. Finally there is a chapter on Hankel norm approximation for the case of scalar rational functions which allows the reader to access ideas and results on the frontier of current research.
Author: Edward Formanek
Publisher: American Mathematical Soc.
ISBN: 0821807307
Category : Mathematics
Languages : en
Pages : 65
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Book Description
The theory of polynomial identities, as a well-defined field of study, began with a well-known 1948 article of Kaplansky. The field has since developed along two branches: the structural, which investigates the properties of rings which satisfy a polynomial identity; and the varietal, which investigates the set of polynomials in the free ring which vanish under all specializations in a given ring. This book is based on lectures delivered during an NSF-CBMS Regional Conference, held at DePaul University in July 1990, at which the author was the principal lecturer. The first part of the book is concerned with polynomial identity rings. The emphasis is on those parts of the theory related to n x n matrices, including the major structure theorems and the construction of certain polynomials identities and central polynomials for n x n matrices. The ring of generic matrices and its centre is described. The author then moves on to the invariants of n x n matrices, beginning with the first and second fundamental theorems, which are used to describe the polynomial identities satisfied by n x n matrices. One of the exceptional features of this book is the way it emphasizes the connection between polynomial identities and invariants of n x n matrices. Accessible to those with background at the level of a first-year graduate course in algebra, this book gives readers an understanding of polynomial identity rings and invariant theory, as well as an indication of current problems and research in these areas.
Author: Karin Erdmann
Publisher: Springer
ISBN: 3319919989
Category : Mathematics
Languages : en
Pages : 304
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Book Description
This 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.
Author: Konstant I. Beidar
Publisher: CRC Press
ISBN: 9780824793258
Category : Mathematics
Languages : en
Pages : 546
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Book Description
"Discusses the latest results concerning the area of noncommutative ring theory known as the theory of generalized identities (GIs)--detailing Kharchenko's results on GIs in prime rings, Chuang's extension to antiautomorphisms, and the use of the Beidar-Mikhalev theory of orthogonal completion in the semiprime case. Provides novel proofs of existing results."
