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Irreducible Subgroups Of Exceptional Algebraic Groups
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Book Synopsis Irreducible Subgroups of Exceptional Algebraic Groups by : Donna M. Testerman
Download or read book Irreducible Subgroups of Exceptional Algebraic Groups written by Donna M. Testerman and published by American Mathematical Soc.. This book was released on 1988 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let [italic]Y be a simply-connected, simple algebraic group of exceptional type, defined over an algebraically closed field [italic]k of prime characteristic [italic]p > 0. The main result describes all semisimple, closed connected subgroups of [italic]Y which act irreducibly on some rational [italic]k[italic]Y module [italic]V. This extends work of Dynkin who obtained a similar classification for algebraically closed fields of characteristic 0. The main result has been combined with work of G. Seitz to obtain a classification of the maximal closed connected subgroups of the classical algebraic groups defined over [italic]k.
Book Synopsis The Irreducible Subgroups of Exceptional Algebraic Groups by : Adam R. Thomas
Download or read book The Irreducible Subgroups of Exceptional Algebraic Groups written by Adam R. Thomas and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is a contribution to the study of the subgroup structure of excep-tional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group G is called irreducible if it lies in no proper parabolic subgroup of G. In this paper we com-plete the classification of irreducible connected subgroups of exceptional algebraic groups, providing an explicit set of representatives for the conjugacy classes of such subgroups. Many consequences of this classification are also given. These include results concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible connected subgroups are determined by their composition factors on the adjoint module of G, with one exception. A result of Liebeck and Testerman shows that each irreducible connected sub-group X of G has only finitely many overgroups and hence the overgroups of X form a lattice. We provide tables that give representatives of each conjugacy class of connected overgroups within this lattice structure. We use this to prove results concerning the subgroup structure of G: for example, when the characteristic is 2, there exists a maximal connected subgroup of G containing a conjugate of every irreducible subgroup A1 of G.
Book Synopsis On Non-Generic Finite Subgroups of Exceptional Algebraic Groups by : Alastair J. Litterick
Download or read book On Non-Generic Finite Subgroups of Exceptional Algebraic Groups written by Alastair J. Litterick and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Maximal Subgroups of Exceptional Algebraic Groups by : Gary M. Seitz
Download or read book Maximal Subgroups of Exceptional Algebraic Groups written by Gary M. Seitz and published by American Mathematical Soc.. This book was released on 1991 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let [italic]G be a simple algebraic group of exceptional type over an algebraically closed field of characteristic [italic]p. The subgroups of [italic]G maximal with respect to being closed and connected are determined, although mild restrictions on [italic]p are required in dealing with certain simple subgroups of low rank. For [italic]p = 0 we recover the results of Dynkin.
Book Synopsis Reductive Subgroups of Exceptional Algebraic Groups by : Martin W. Liebeck
Download or read book Reductive Subgroups of Exceptional Algebraic Groups written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 1996 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of simple algebraic groups is important in many areas of mathematics. The authors of this book investigate the subgroups of certain types of simple algebraic groups and obtain a complete description of all those subgroups which are themselves simple. This description is particularly useful in understanding centralizers of subgroups and restrictions of representations.
Book Synopsis $A_1$ Subgroups of Exceptional Algebraic Groups by : Ross Lawther
Download or read book $A_1$ Subgroups of Exceptional Algebraic Groups written by Ross Lawther and published by American Mathematical Soc.. This book was released on 1999 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in group theory and genralizations
Book Synopsis Irreducible Almost Simple Subgroups of Classical Algebraic Groups by : Timothy C. Burness
Download or read book Irreducible Almost Simple Subgroups of Classical Algebraic Groups written by Timothy C. Burness and published by American Mathematical Soc.. This book was released on 2015-06-26 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a nontrivial -restricted irreducible tensor indecomposable rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where and is a disconnected almost simple positive-dimensional closed subgroup of acting irreducibly on . Moreover, by combining this result with earlier work, they complete the classification of the irreducible triples where is a simple algebraic group over , and is a maximal closed subgroup of positive dimension.
Book Synopsis Algebraic Groups and Their Representations by : R.W. Carter
Download or read book Algebraic Groups and Their Representations written by R.W. Carter and published by Springer Science & Business Media. This book was released on 1998-08-31 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles by 20 leading workers in the field of algebraic groups and related finite groups. Articles on representation theory are written by Andersen on tilting modules, Carter on canonical bases, Cline, Parshall and Scott on endomorphism algebras, James and Kleshchev on the symmetric group, Littelmann on the path model, Lusztig on homology bases, McNinch on semisimplicity in prime characteristic, Robinson on block theory, Scott on Lusztig's character formula, and Tanisaki on highest weight modules. Articles on subgroup structure are written by Seitz and Brundan on double cosets, Liebeck on exceptional groups, Saxl on subgroups containing special elements, and Guralnick on applications of subgroup structure. Steinberg gives a new, short proof of the isomorphism and isogeny theorems for reductive groups. Aschbacher discusses the classification of quasithin groups and Borovik the classification of groups of finite Morley rank. Audience: The book contains accounts of many recent advances and will interest research workers and students in the theory of algebraic groups and related areas of mathematics.
Book Synopsis The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups by : Martin W. Liebeck
Download or read book The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 2004 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intends to complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This title follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small.
Book Synopsis Irreducible Geometric Subgroups of Classical Algebraic Groups by : Timothy C. Burness,
Download or read book Irreducible Geometric Subgroups of Classical Algebraic Groups written by Timothy C. Burness, and published by American Mathematical Soc.. This book was released on 2016-01-25 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a non-trivial irreducible tensor-indecomposable -restricted rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where is a disconnected maximal positive-dimensional closed subgroup of preserving a natural geometric structure on .
Book Synopsis Groups, Combinatorics and Geometry by : Martin W. Liebeck
Download or read book Groups, Combinatorics and Geometry written by Martin W. Liebeck and published by Cambridge University Press. This book was released on 1992-09-10 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers on the subject of the classification of finite simple groups.
Book Synopsis The Maximal Subgroups of Classical Algebraic Groups by : Gary M. Seitz
Download or read book The Maximal Subgroups of Classical Algebraic Groups written by Gary M. Seitz and published by American Mathematical Soc.. This book was released on 1987 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let [italic]V be a finite dimensional vector space over an algebraically closed field of characteristic p [greater than] 0 and let G = SL([italic]V), Sp([italic]V), or SO([italic]V). The main result describes all closed, connected, overgroups of [italic]X in SL([italic]V), assuming [italic]X is a closed, connected, irreducible subgroup of G.
Book Synopsis Groups St Andrews 2017 in Birmingham by : C. M. Campbell
Download or read book Groups St Andrews 2017 in Birmingham written by C. M. Campbell and published by Cambridge University Press. This book was released on 2019-04-11 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings of 'Groups St Andrews 2017' provide a snapshot of the state-of-the-art in contemporary group theory.
Book Synopsis Groups of Lie Type and Their Geometries by : William M. Kantor
Download or read book Groups of Lie Type and Their Geometries written by William M. Kantor and published by Cambridge University Press. This book was released on 1995-01-12 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Silk Hope, NC is a buoyant and moving parable in which two good women find, among the hidden, forgotten virtues of the past, a sustenance to carry them into the future.
Book Synopsis Finite and Locally Finite Groups by : B. Hartley
Download or read book Finite and Locally Finite Groups written by B. Hartley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups held in Istanbul, Turkey, 14-27 August 1994, at which there were about 90 participants from some 16 different countries. The ASI received generous financial support from the Scientific Affairs Division of NATO. INTRODUCTION A locally finite group is a group in which every finite set of elements is contained in a finite subgroup. The study of locally finite groups began with Schur's result that a periodic linear group is, in fact, locally finite. The simple locally finite groups are of particular interest. In view of the classification of the finite simple groups and advances in representation theory, it is natural to pursue classification theorems for simple locally finite groups. This was one of the central themes of the Istanbul conference and significant progress is reported herein. The theory of simple locally finite groups intersects many areas of group theory and representation theory, so this served as a focus for several articles in the volume. Every simple locally finite group has what is known as a Kegel cover. This is a collection of pairs {(G , Ni) liE I}, where I is an index set, each group Gi is finite, i Ni
Book Synopsis Linear Algebraic Groups and Finite Groups of Lie Type by : Gunter Malle
Download or read book Linear Algebraic Groups and Finite Groups of Lie Type written by Gunter Malle and published by Cambridge University Press. This book was released on 2011-09-08 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.
Book Synopsis Proceedings of the St. Petersburg Mathematical Society, Volume I by : O. A. Ladyzhenskaya Anatoli_ Moiseevich Vershik
Download or read book Proceedings of the St. Petersburg Mathematical Society, Volume I written by O. A. Ladyzhenskaya Anatoli_ Moiseevich Vershik and published by American Mathematical Soc.. This book was released on 1993-03-22 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the inaugural volume of a new book series published under the auspices of the St. Petersburg Mathematical Society. The book contains contributions by some of the leading mathematicians in St. Petersburg. Ranging over a wide array of topics, these papers testify to the diverse interests and productive mathematical life of the St. Petersburg Mathematical Society.
