Last edited by Kalkis
Sunday, August 2, 2020 | History

3 edition of Linear algebraic groups and finite groups of lie type found in the catalog.

Linear algebraic groups and finite groups of lie type

by Gunter Malle

  • 347 Want to read
  • 28 Currently reading

Published by Cambridge University Press in Cambridge, New York .
Written in English

    Subjects:
  • Linear algebraic groups,
  • Lie algebras

  • Edition Notes

    Includes bibliographical references (p. [301]-304) and index.

    StatementGunter Malle, Donna Testerman
    SeriesCambridge studies in advanced mathematics -- 133, Cambridge studies in advanced mathematics -- 133.
    ContributionsTesterman, Donna M., 1960-
    Classifications
    LC ClassificationsQA179 .M35 2011
    The Physical Object
    Paginationxii, 309 p. :
    Number of Pages309
    ID Numbers
    Open LibraryOL25151738M
    ISBN 101107008549
    ISBN 109781107008540
    LC Control Number2011275249
    OCLC/WorldCa709837768

    In book: Representation Theory of Finite Groups: a Guidebook, pp Linear algebraic groups and finite groups of Lie type In the building of a finite group of Lie type we consider the. In book: Lie Algebras and Algebraic Groups. Linear algebraic groups, Graduate texts in math We investigate structural properties and numerical invariants of the finite-dimensional solvable.

      The proof here follows the same line as the proof in [9]. Let L be a finite simple group of Lie type defined over a finite field GF(q) with q = rm elements (r a prime) and let G be a simply connected simple linear algebraic group with endomorphism a such that L^ (GJZ(Ga)', where Ga denotes the fixed points of a on G and Z(Ga) = Z the center of Ga. Find many great new & used options and get the best deals for Cambridge Studies in Advanced Mathematics Ser.: Linear Algebraic Groups and Finite Groups of Lie Type by Donna Testerman and Gunter Malle (, Hardcover) at the best online prices at eBay! Free shipping for many products!

    Linear algebraic group; Reductive group; and all finite simple groups of Lie type have linear representations that are "small" compared to the size of the group. All sporadic groups other than the monster also have linear representations small enough that they are easy to work with on a computer (the next hardest case after the monster is.   JOURNAL OF ALGE () Finite Simple Groups of Lie Type Have Non-principal p-Blocks, p2 PETER BROCKHAUS AND GERHARD 0. MICHLER Department of Mathematics, University of Essen, Essen, West Germany Communicated by B. .


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Linear algebraic groups and finite groups of lie type by Gunter Malle Download PDF EPUB FB2

The aim of the course was to introduce an audience consisting mainly of PhD students and postdoctoral researchers working in finite group theory and neighboring areas to results on the subgroup structure of linear algebraic groups and the related finite groups of Lie type.

Linear Algebraic Groups and Finite Groups of Lie Type (Cambridge Studies in Advanced Mathematics Book ) - Kindle edition by Malle, Gunter, Testerman, Donna. Download it once and read it on your Kindle device, PC, phones or tablets.

Use features like bookmarks, note taking and highlighting while reading Linear Algebraic Groups and Finite Groups of Lie Type (Cambridge Manufacturer: Cambridge University Press. 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 Linear algebraic groups and finite groups of lie type book groups of Lie type as a consequence of the structural results on 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 by: 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. LINEAR ALGEBRAIC GROUPS AND FINITE GROUPS OF LIE TYPE 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 remaining chapters treat only affine algebraic groups. After a review of the Tannakian philosophy, there are short accounts of Lie algebras and finite group schemes. Solvable algebraic groups are studied in detail in Chapters There are 17 families of simple groups, the alternating groups and 16 families of “Lie type”.

These in turn are broken up into subfamilies in several different ways. There are, first, the historical breakdowns, 6 families of “classical groups”, the projective special linear groups over finite fields, the orthogonal groups, (three types.

iAG: Algebraic Groups. The theory of group schemes of finite type over a field: CUPpp. info: LAG: Lie Algebras, Algebraic Groups, and Lie Groups. "This book provides a concise introduction to the theory of linear algebraic groups over an algebraically closed field (of arbitrary charachteristic) and the closely related finite groups of Lie type.

Although there are several good books covering a similar range of topics, some important recent developments are treated here for the first by: The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups.

They emphasize the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced from it. They also discuss Deligne-Lusztig induction.

This will be the first elementary treatment of this material in book form and will be. The book under review has as its main goal to give a systematic exposition of the subgroup structure of the finite groups of Lie type based on the general properties of linear algebraic groups.

In order to do this, the authors first develop the basic theory of linear algebraic groups, assuming that the reader is familiar with the elements of. Linear Algebraic Group and Finite Groups of Lie Type Let k be an algebraically closed field.

A linear algebraic group over k is a closed subgroup of the General Linear Group over k. Abstract. Let G be a reductive connected algebraic group over an algebraic closure of a finite field of characteristic p.

Let F be a Frobenius endomorphism on G and write G: = G F for the corresponding finite group of Lie type. Abstract. The final chapter is the representation theory of groups of Lie type, both in defining and non-defining characteristics.

The first section deals with defining characteristic representations, introducing highest weight modules, Weyl modules, and building up to the Lusztig conjecture, with a diversion into Ext 1 between simple modules for the algebraic group and the finite group.

The list of finite simple groups of Lie type has been understood for half a century, modulo some differences in notation (and identifications between some of the very small groups coming from different Lie types). Call this collection of isomorphism classes of finite groups $\mathcal{S}$.

But it's not clear to me that there is a similar consensus about the meaning of "finite group of Lie type". Algebraic groups play much the same role for algebraists as Lie groups play for analysts.

This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that includes the structure theory of semisimple algebraic groups, and is written in the language of modern algebraic geometry.

"This book provides a concise introduction to the theory of linear algebraic groups over an algebraically closed field (of arbitrary charachteristic) and the closely related finite groups of Lie Although there are several good books covering a similar range of topics, some important recent developments are treated here for the first time.

Finite groups of Lie type Steinberg [Endomorphisms of linear algebraic groups, ] has studied the situation where G is a reductive algebraic group over an algebraically closed eld and F is an algebraic endomorphism such that GF (the xed points) is nite. Then GF is called a nite group of Lie type.

He has classi ed the possibilities. Get this from a library. Linear Algebraic Groups and Finite Groups of Lie Type. [Gunter Malle; Donna Testerman] -- The first textbook on the subgroup structure, in particular maximal subgroups, for both algebraic and finite groups of Lie type.

If $\mathfrak{g}$ is the Lie algebra of an affine algebraic group then it must be ad-algebraic, ie. its image in $\operatorname{End}(\mathfrak{g})$ under the adjoint representation must be an algebraic subalgebra.

An example of a non-ad-algebraic Lie algebra is given on pg. of Lie Algebras and Algebraic Groups, by Tauvel and Yu.In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four broad classes described below.

The classification theorem states that the list of finite simple groups consists of 18 countably infinite families, plus 26 exceptions that do not follow such a systematic pattern. The finite simple groups are important because. Presently (s) the apparatus of Lie algebras has been perceived not only as a useful and powerful tool in the linearization of group-theoretic problems (whether in the theory of Lie groups or in the theory of algebraic groups, cf.

Algebraic group, which to a significant extent absorbs it and extremely outgrows it, or in the theory of finite.