Lectures On Block Theory
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Author | : Burkhard Külshammer |
Publisher | : Cambridge University Press |
Total Pages | : 120 |
Release | : 1991-04-04 |
Genre | : Mathematics |
ISBN | : 9780521405652 |
Block theory is a part of the theory of modular representation of finite groups and deals with the algebraic structure of blocks. In this volume Burkhard Külshammer starts with the classical structure theory of finite dimensional algebras, and leads up to Puigs main result on the structure of the so called nilpotent blocks, which he discusses in the final chapter. All the proofs in the text are given clearly and in full detail, and suggestions for further reading are also included. For researchers and graduate students interested in group theory or representation theory, this book will form an excellent self contained introduction to the theory of blocks.
Author | : Mark Pollicott |
Publisher | : Cambridge University Press |
Total Pages | : 176 |
Release | : 1993-02-04 |
Genre | : Mathematics |
ISBN | : 9780521435932 |
These lecture notes provide a unique introduction to Pesin theory and its applications.
Author | : Igor Dolgachev |
Publisher | : Cambridge University Press |
Total Pages | : 244 |
Release | : 2003-08-07 |
Genre | : Mathematics |
ISBN | : 9780521525480 |
The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.
Author | : Markus Linckelmann |
Publisher | : Cambridge University Press |
Total Pages | : 523 |
Release | : 2018 |
Genre | : Blocks |
ISBN | : 1108425909 |
Author | : Markus Linckelmann |
Publisher | : Cambridge University Press |
Total Pages | : 527 |
Release | : 2018-05-24 |
Genre | : Mathematics |
ISBN | : 1108575315 |
This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.
Author | : Thomas Peterfalvi |
Publisher | : Cambridge University Press |
Total Pages | : 166 |
Release | : 2000-02-28 |
Genre | : Mathematics |
ISBN | : 9780521646604 |
The famous and important theorem of W. Feit and J. G. Thompson states that every group of odd order is solvable, and the proof of this has roughly two parts. The first part appeared in Bender and Glauberman's Local Analysis for the Odd Order Theorem which was number 188 in this series. This book provides the character-theoretic second part and thus completes the proof. All researchers in group theory should have a copy of this book in their library.
Author | : C. M. Campbell |
Publisher | : Cambridge University Press |
Total Pages | : 320 |
Release | : 1995-03-16 |
Genre | : Mathematics |
ISBN | : 0521477492 |
Representing the wealth and diversity of group theory for experienced researchers as well as new postgraduates, this two-volume book contains selected papers from the international conference which was held at University College Galway in August 1993.
Author | : Fernando Q. Gouvêa |
Publisher | : Cambridge University Press |
Total Pages | : 185 |
Release | : 1995-05-11 |
Genre | : Mathematics |
ISBN | : 0521498341 |
This book is concerned with the arithmetic of diagonal hypersurfaces over finite fields.
Author | : Markus Linckelmann |
Publisher | : Cambridge University Press |
Total Pages | : 523 |
Release | : 2018-05-24 |
Genre | : Mathematics |
ISBN | : 1108562582 |
This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.
Author | : A. Martsinkovsky |
Publisher | : Cambridge University Press |
Total Pages | : 148 |
Release | : 1997-05-15 |
Genre | : Mathematics |
ISBN | : 9780521577892 |
For any researcher working in representation theory, algebraic or arithmetic geometry.