Polynomial Invariants of Finite Groups

This is the first book to deal with invariant theory and the representations of finite groups.

Author: D. J. Benson

Publisher: Cambridge University Press

ISBN: 0521458862

Category: Mathematics

Page: 118

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This is the first book to deal with invariant theory and the representations of finite groups.

Polynomial Invariants of Finite Groups

This is the first book to deal with invariant theory and the representations of finite groups.

Author: D. J. Benson

Publisher:

ISBN: 1107366941

Category: Divisor theory

Page: 132

View: 752

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This is the first book to deal with invariant theory and the representations of finite groups.

Multiplicative Ideal Theory and Factorization Theory

126, 217 (2007) D.J. Benson, Polynomial Invariants of Finite Groups, vol. 190, London Mathematical Society Lecture Notes Series (Cambridge University Press, Cambridge, 1993) 5. G. Bhowmik, J.-C. Schlage-Puchta, Davenport's constant for ...

Author: Scott Chapman

Publisher: Springer

ISBN: 9783319388557

Category: Mathematics

Page: 407

View: 199

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This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.

On Characters of Finite Groups

38, 318–342 (1976) [Ben93] D. Benson, Polynomial Invariants of Finite Groups, London Mathematical Society Lecture Note Series (Cambridge University Press, Cambridge, 1993) [Bes97] D. Bessis, Sur le corps de définition d'un groupe de ...

Author: Michel Broué

Publisher: Springer

ISBN: 9789811068782

Category: Mathematics

Page: 246

View: 899

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This book explores the classical and beautiful character theory of finite groups. It does it by using some rudiments of the language of categories. Originally emerging from two courses offered at Peking University (PKU), primarily for third-year students, it is now better suited for graduate courses, and provides broader coverage than books that focus almost exclusively on groups. The book presents the basic tools, notions and theorems of character theory (including a new treatment of the control of fusion and isometries), and introduces readers to the categorical language at several levels. It includes and proves the major results on characteristic zero representations without any assumptions about the base field. The book includes a dedicated chapter on graded representations and applications of polynomial invariants of finite groups, and its closing chapter addresses the more recent notion of the Drinfeld double of a finite group and the corresponding representation of GL_2(Z).

Computational Invariant Theory

Larry Smith, Polynomial Invariants of Finite Groups, A. K. Peters, Wellesley, Mass. 1995. ... Igor Dolgachev, Lectures on Invariant Theory, London Mathematical Society Lecture Note Series 296, Cambridge University Press, Cambridge 2003.

Author: Harm Derksen

Publisher: Springer

ISBN: 9783662484227

Category: Mathematics

Page: 366

View: 601

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This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest. More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimi r Popov, and an addendum by Norbert A'Campo and Vladimir Popov.

Finite Fields with Applications to Coding Theory Cryptography and Related Areas

Landrock P., Finite Group Algebras and their Modules, LMS Lecture Note Series, Cambridge University Press (1984). Smith L., E. Noether's bound in the invariant theory of finite groups, Arch. Math. 66, 89–92, (1995). Smith L., Polynomial ...

Author: Gary L. Mullen

Publisher: Springer Science & Business Media

ISBN: 9783642594359

Category: Mathematics

Page: 335

View: 483

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The Sixth International Conference on Finite Fields and Applications, Fq6, held in the city of Oaxaca, Mexico, from May 21-25, 2001, continued a series of biennial international conferences on finite fields. This volume documents the steadily increasing interest in this topic. Finite fields are an important tool in discrete mathematics and its applications cover algebraic geometry, coding theory, cryptology, design theory, finite geometries, and scientific computation, among others. An important feature is the interplay between theory and applications which has led to many new perspectives in research on finite fields and other areas. This interplay has been emphasized in this series of conferences and certainly was reflected in Fq6. This volume offers up-to-date original research papers by leading experts in the area.

Recent Developments in Representation Theory

... Down-up algebras, J. Algebra 209 (1998), no. 1, 305– 344, DOI 10.1006/jabr.1998.7511. MR1652138 (2000e:06001a) D. J. Benson, Polynomial invariants of finite groups, London Mathematical Society Lecture Note Series ...

Author: Alex Martsinkovsky

Publisher: American Mathematical Soc.

ISBN: 9781470419554

Category: Associative rings

Page: 249

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This volume contains selected expository lectures delivered at the Maurice Auslander Distinguished Lectures and International Conference, held May 1–6, 2014, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Several significant developments of the last decade in representation theory of finite-dimensional algebras are related to combinatorics. Three of the five lectures in this volume deal, respectively, with the Catalan combinatorics, the combinatorics of Gelfand-Zetlin polytopes, and the combinatorics of tilting modules. The remaining papers present history and recent advances in the study of left orders in left Artinian rings and a survey on invariant theory of Artin-Schelter regular algebras.

Recent Advances in Representation Theory Quantum Groups Algebraic Geometry and Related Topics

MR1317096 (96f:20082) D. J. Benson, Polynomial invariants of finite groups, London Mathematical Society Lecture Note Series, vol. 190, Cambridge University Press, Cambridge, 1993. MR1249931 (94j:13003) J. Cameron Atkins, The invariant ...

Author: Pramod M. Achar

Publisher: American Mathematical Society

ISBN: 9780821898529

Category: Mathematics

Page: 280

View: 808

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This volume contains the proceedings of two AMS Special Sessions "Geometric and Algebraic Aspects of Representation Theory" and "Quantum Groups and Noncommutative Algebraic Geometry" held October 13–14, 2012, at Tulane University, New Orleans, Louisiana. Included in this volume are original research and some survey articles on various aspects of representations of algebras including Kac—Moody algebras, Lie superalgebras, quantum groups, toroidal algebras, Leibniz algebras and their connections with other areas of mathematics and mathematical physics.

Geometric and Topological Aspects of the Representation Theory of Finite Groups

D. J. Benson, Polynomial invariants of finite groups, London Mathematical Society Lecture Note Series, vol. 190, Cambridge University Press, Cambridge, 1993. MR 1249931. 11. A. D. Elmendorf, I. Kriz, M. A. Mandell, and J. P. May, Rings, ...

Author: Jon F. Carlson

Publisher: Springer

ISBN: 9783319940335

Category: Mathematics

Page: 495

View: 275

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These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.