Invariant Theory And Superalgebras

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Invariant Theory and Superalgebras

Author : Frank D. Grosshans
Publisher : American Mathematical Soc.
ISBN 13 : 0821807196
Total Pages : 106 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Invariant Theory and Superalgebras by : Frank D. Grosshans

Download or read book Invariant Theory and Superalgebras written by Frank D. Grosshans and published by American Mathematical Soc.. This book was released on 1987-12-31 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings the reader to the frontiers of research in some topics in superalgebras and symbolic method in invariant theory. Superalgebras are algebras containing positively-signed and negatively-signed variables. One of the book's major results is an extension of the standard basis theorem to superalgebras. This extension requires a rethinking of some basic concepts of linear algebra, such as matrices and coordinate systems, and may lead to an extension of the entire apparatus of linear algebra to ``signed'' modules. The authors also present the symbolic method for the invariant theory of symmetric and of skew-symmetric tensors. In both cases, the invariants are obtained from the symbolic representation by applying what the authors call the umbral operator. This operator can be used to systematically develop anticommutative analogs of concepts of algebraic geometry, and such results may ultimately turn out to be the main byproduct of this investigation. While it will be of special interest to mathematicians and physicists doing research in superalgebras, invariant theory, straightening algorithms, Young bitableaux, and Grassmann's calculus of extension, the book starts from basic principles and should therefore be accessible to those who have completed the standard graduate level courses in algebra and/or combinatorics.

Algebraic Combinatorics and Computer Science

Author : H. Crapo
Publisher : Springer Science & Business Media
ISBN 13 : 9788847000780
Total Pages : 564 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis Algebraic Combinatorics and Computer Science by : H. Crapo

Download or read book Algebraic Combinatorics and Computer Science written by H. Crapo and published by Springer Science & Business Media. This book was released on 2001-01-01 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, dedicated to the memory of Gian-Carlo Rota, is the result of a collaborative effort by his friends, students and admirers. Rota was one of the great thinkers of our times, innovator in both mathematics and phenomenology. I feel moved, yet touched by a sense of sadness, in presenting this volume of work, despite the fear that I may be unworthy of the task that befalls me. Rota, both the scientist and the man, was marked by a generosity that knew no bounds. His ideas opened wide the horizons of fields of research, permitting an astonishing number of students from all over the globe to become enthusiastically involved. The contagious energy with which he demonstrated his tremendous mental capacity always proved fresh and inspiring. Beyond his renown as gifted scientist, what was particularly striking in Gian-Carlo Rota was his ability to appreciate the diverse intellectual capacities of those before him and to adapt his communications accordingly. This human sense, complemented by his acute appreciation of the importance of the individual, acted as a catalyst in bringing forth the very best in each one of his students. Whosoever was fortunate enough to enjoy Gian-Carlo Rota's longstanding friendship was most enriched by the experience, both mathematically and philosophically, and had occasion to appreciate son cote de bon vivant. The book opens with a heartfelt piece by Henry Crapo in which he meticulously pieces together what Gian-Carlo Rota's untimely demise has bequeathed to science.

Lie Superalgebras and Enveloping Algebras

Author : Ian Malcolm Musson
Publisher : American Mathematical Soc.
ISBN 13 : 0821868675
Total Pages : 512 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lie Superalgebras and Enveloping Algebras by : Ian Malcolm Musson

Download or read book Lie Superalgebras and Enveloping Algebras written by Ian Malcolm Musson and published by American Mathematical Soc.. This book was released on 2012-04-04 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. This book develops the theory of Lie superalgebras, their enveloping algebras, and their representations. The book begins with five chapters on the basic properties of Lie superalgebras, including explicit constructions for all the classical simple Lie superalgebras. Borel subalgebras, which are more subtle in this setting, are studied and described. Contragredient Lie superalgebras are introduced, allowing a unified approach to several results, in particular to the existence of an invariant bilinear form on $\mathfrak{g}$. The enveloping algebra of a finite dimensional Lie superalgebra is studied as an extension of the enveloping algebra of the even part of the superalgebra. By developing general methods for studying such extensions, important information on the algebraic structure is obtained, particularly with regard to primitive ideals. Fundamental results, such as the Poincare-Birkhoff-Witt Theorem, are established. Representations of Lie superalgebras provide valuable tools for understanding the algebras themselves, as well as being of primary interest in applications to other fields. Two important classes of representations are the Verma modules and the finite dimensional representations. The fundamental results here include the Jantzen filtration, the Harish-Chandra homomorphism, the Sapovalov determinant, supersymmetric polynomials, and Schur-Weyl duality. Using these tools, the center can be explicitly described in the general linear and orthosymplectic cases. In an effort to make the presentation as self-contained as possible, some background material is included on Lie theory, ring theory, Hopf algebras, and combinatorics.

Algorithms in Invariant Theory

Author : Bernd Sturmfels
Publisher : Springer Science & Business Media
ISBN 13 : 3211774173
Total Pages : 202 pages
Book Rating : 4.2/5 (117 download)

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Book Synopsis Algorithms in Invariant Theory by : Bernd Sturmfels

Download or read book Algorithms in Invariant Theory written by Bernd Sturmfels and published by Springer Science & Business Media. This book was released on 2008-06-17 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to research ideas, hints for applications, outlines and details of algorithms, examples and problems.

The Invariant Theory of Matrices

Author : Corrado De Concini
Publisher : American Mathematical Soc.
ISBN 13 : 147044187X
Total Pages : 162 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Invariant Theory of Matrices by : Corrado De Concini

Download or read book The Invariant Theory of Matrices written by Corrado De Concini and published by American Mathematical Soc.. This book was released on 2017-11-16 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving (1) the first fundamental theorem that describes a set of generators in the ring of invariants, and (2) the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.

Dualities and Representations of Lie Superalgebras

Author : Shun-Jen Cheng
Publisher : American Mathematical Soc.
ISBN 13 : 0821891189
Total Pages : 323 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Dualities and Representations of Lie Superalgebras by : Shun-Jen Cheng

Download or read book Dualities and Representations of Lie Superalgebras written by Shun-Jen Cheng and published by American Mathematical Soc.. This book was released on 2012 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a systematic account of the structure and representation theory of finite-dimensional complex Lie superalgebras of classical type and serves as a good introduction to representation theory of Lie superalgebras. Several folklore results are rigorously proved (and occasionally corrected in detail), sometimes with new proofs. Three important dualities are presented in the book, with the unifying theme of determining irreducible characters of Lie superalgebras. In order of increasing sophistication, they are Schur duality, Howe duality, and super duality. The combinatorics of symmetric functions is developed as needed in connections to Harish-Chandra homomorphism as well as irreducible characters for Lie superalgebras. Schur-Sergeev duality for the queer Lie superalgebra is presented from scratch with complete detail. Howe duality for Lie superalgebras is presented in book form for the first time. Super duality is a new approach developed in the past few years toward understanding the Bernstein-Gelfand-Gelfand category of modules for classical Lie superalgebras. Super duality relates the representation theory of classical Lie superalgebras directly to the representation theory of classical Lie algebras and thus gives a solution to the irreducible character problem of Lie superalgebras via the Kazhdan-Lusztig polynomials of classical Lie algebras.

Classical Invariant Theory

Author : Peter J. Olver
Publisher : Cambridge University Press
ISBN 13 : 9780521558211
Total Pages : 308 pages
Book Rating : 4.5/5 (582 download)

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Book Synopsis Classical Invariant Theory by : Peter J. Olver

Download or read book Classical Invariant Theory written by Peter J. Olver and published by Cambridge University Press. This book was released on 1999-01-13 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a self-contained introduction to the results and methods in classical invariant theory.

The Theory of Lie Superalgebras

Author : M. Scheunert
Publisher : Springer
ISBN 13 : 3540352864
Total Pages : 280 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis The Theory of Lie Superalgebras by : M. Scheunert

Download or read book The Theory of Lie Superalgebras written by M. Scheunert and published by Springer. This book was released on 2006-11-15 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Theory and Geometry

Author : Jean-Luc Brylinski
Publisher : Springer Science & Business Media
ISBN 13 : 1461202612
Total Pages : 629 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Lie Theory and Geometry by : Jean-Luc Brylinski

Download or read book Lie Theory and Geometry written by Jean-Luc Brylinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Bertram Kostant on the occasion of his 65th birthday, is a collection of 22 invited papers by leading mathematicians working in Lie theory, geometry, algebra, and mathematical physics. Kostant’s fundamental work in all these areas has provided deep new insights and connections, and has created new fields of research. The papers gathered here present original research articles as well as expository papers, broadly reflecting the range of Kostant’s work.

Invariant Theory and Superalgebras

Author : Frank D. Grosshans
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889138
Total Pages : 108 pages
Book Rating : 4.8/5 (891 download)

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Book Synopsis Invariant Theory and Superalgebras by : Frank D. Grosshans

Download or read book Invariant Theory and Superalgebras written by Frank D. Grosshans and published by American Mathematical Soc.. This book was released on 1987-01-01 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Groups and Invariant Theory

Author : Ėrnest Borisovich Vinberg
Publisher : American Mathematical Soc.
ISBN 13 : 9780821837337
Total Pages : 284 pages
Book Rating : 4.8/5 (373 download)

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Book Synopsis Lie Groups and Invariant Theory by : Ėrnest Borisovich Vinberg

Download or read book Lie Groups and Invariant Theory written by Ėrnest Borisovich Vinberg and published by American Mathematical Soc.. This book was released on 2005 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, devoted to the 70th birthday of A. L. Onishchik, contains a collection of articles by participants in the Moscow Seminar on Lie Groups and Invariant Theory headed by E. B. Vinberg and A. L. Onishchik. The book is suitable for graduate students and researchers interested in Lie groups and related topics.

Invariant Theory and Tableaux

Author : Dennis Stanton
Publisher : Springer
ISBN 13 :
Total Pages : 320 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Invariant Theory and Tableaux by : Dennis Stanton

Download or read book Invariant Theory and Tableaux written by Dennis Stanton and published by Springer. This book was released on 1990 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume stems from a workshop held for the Applied Combinatorics program in March 1988. The central idea of the workshop was the recent interplay of the classical analysis of q-series, and the combinatorial analysis of partitions of integers. Many related topics were discussed, including orthogonal polynomials, the Macdonald conjectures for root systems, and related integrals. Those people interested in combinatorial enumeration and special functions will find this volume of interest. Recent applications of q-series (and related functions) to exactly solvable statistical mechanics models and to statistics makes this volume of interest to non-specialists. Included are several expository papers, and a series of papers on new work on the unimodality of the q-binomial coefficient.

Introduction to Vassiliev Knot Invariants

Author : S. Chmutov
Publisher : Cambridge University Press
ISBN 13 : 1107020832
Total Pages : 521 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Introduction to Vassiliev Knot Invariants by : S. Chmutov

Download or read book Introduction to Vassiliev Knot Invariants written by S. Chmutov and published by Cambridge University Press. This book was released on 2012-05-24 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed exposition of the theory with an emphasis on its combinatorial aspects.

Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras

Author : Vyjayanthi Chari
Publisher : American Mathematical Soc.
ISBN 13 : 082180748X
Total Pages : 172 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras by : Vyjayanthi Chari

Download or read book Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras written by Vyjayanthi Chari and published by American Mathematical Soc.. This book was released on 1997 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers dedicated to Richard E. Block, whose research has been largely devoted to the study of Lie algebras of prime characteristic (specifically the classification of simple Lie algebras). The volume presents proceedings of a conference held at the University of California at Riverside in February 1994 on the occasion of his retirement. The conference focused on the interplay between the theory of Lie algebras of prime characteristic, quantum groups, and Lie superalgebras. Titles in this series are co-published with International Press, Cambridge, MA, USA.

Perspectives in Lie Theory

Author : Filippo Callegaro
Publisher : Springer
ISBN 13 : 3319589717
Total Pages : 465 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Perspectives in Lie Theory by : Filippo Callegaro

Download or read book Perspectives in Lie Theory written by Filippo Callegaro and published by Springer. This book was released on 2017-12-07 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.

Invariant Theory

Author : Robert M. Fossum
Publisher : American Mathematical Soc.
ISBN 13 : 0821850946
Total Pages : 610 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Invariant Theory by : Robert M. Fossum

Download or read book Invariant Theory written by Robert M. Fossum and published by American Mathematical Soc.. This book was released on 1989 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Invariant Theory, held in Denton, Texas in the fall of 1986; also included are several invited papers in this area. The purpose of the conference was to exchange ideas on recent developments in algebraic group actions on algebraic varieties. The papers fall into three main categories: actions of linear algebraic groups; flag manifolds and invariant theory; and representation theory and invariant theory. This book is likely to find a wide audience, for invariant theory is connected to a range of mathematical fields, such as algebraic groups, algebraic geometry, commutative algebra, and representation theory.

Algebras and Representation Theory

Author : Karin Erdmann
Publisher : Springer
ISBN 13 : 3319919989
Total Pages : 304 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Algebras and Representation Theory by : Karin Erdmann

Download or read book Algebras and Representation Theory written by Karin Erdmann and published by Springer. This book was released on 2018-09-07 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.