Invariant Theory And Superalgebras
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Invariant Theory And Superalgebras
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Author : Frank D. Grosshans
language : en
Publisher: American Mathematical Soc.
Release Date : 1987-12-31
Invariant Theory And Superalgebras written by Frank D. Grosshans and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-12-31 with Mathematics categories.
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.
Invariant Theory And Superalgebras
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Author : Frank D. Grosshans
language : en
Publisher: American Mathematical Soc.
Release Date : 1987-01-01
Invariant Theory And Superalgebras written by Frank D. Grosshans and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-01-01 with Mathematics categories.
Classical Invariant Theory
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Author : Peter J. Olver
language : en
Publisher: Cambridge University Press
Release Date : 1999-01-13
Classical Invariant Theory written by Peter J. Olver and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-13 with Mathematics categories.
The book is a self-contained introduction to the results and methods in classical invariant theory.
Algorithms In Invariant Theory
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Author : Bernd Sturmfels
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-17
Algorithms In Invariant Theory written by Bernd Sturmfels and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-17 with Mathematics categories.
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.
Invariant Theory And Tableaux
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Author : Dennis Stanton
language : en
Publisher: Springer
Release Date : 1990
Invariant Theory And Tableaux written by Dennis Stanton and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
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.
Lie Groups And Invariant Theory
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Author : Ėrnest Borisovich Vinberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Lie Groups And Invariant Theory written by Ėrnest Borisovich Vinberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.
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
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Author : Robert M. Fossum
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Invariant Theory written by Robert M. Fossum and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
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.
Algebraic Combinatorics And Computer Science
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Author : H. Crapo
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-01-01
Algebraic Combinatorics And Computer Science written by H. Crapo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
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.
Algebraic Combinatorics And Computer Science
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Author : H. Crapo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Combinatorics And Computer Science written by H. Crapo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Symmetry Representations And Invariants
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Author : Roe Goodman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-30
Symmetry Representations And Invariants written by Roe Goodman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-30 with Mathematics categories.
Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: (1) Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus; (2) Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux); (3) Self-contained chapters, appendices, comprehensive bibliography; (4) More than 350 exercises (most with detailed hints for solutions) further explore main concepts; (5) Serves as an excellent main text for a one-year course in Lie group theory; (6) Benefits physicists as well as mathematicians as a reference work.