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1 edition of Centres of centralizers of unipotent elements in simple algebraic groups found in the catalog.

Centres of centralizers of unipotent elements in simple algebraic groups

R. Lawther

# Centres of centralizers of unipotent elements in simple algebraic groups

## by R. Lawther

Written in English

Subjects:
• Linear algebraic groups

• Edition Notes

Classifications The Physical Object Statement R. Lawther, D.M. Testerman Series Memoirs of the American Mathematical Society -- no. 988 Contributions Testerman, Donna M., 1960- LC Classifications QA179 .L39 2010 Pagination v, 188 p. ; Number of Pages 188 Open Library OL24893317M ISBN 10 9780821847695 LC Control Number 2010046991

Algebraic groups play much the same role for algebraists that Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields, including the structure theory of semisimple algebraic groups, written in the language of modern algebraic . [13] Simion, I.I., Double centralizers of unipotent elements in simple algebraic groups of type G 2, F 4 and E 6, J. Algebra, (), { [14] Simion, I.I., Double centralizers of unipotent elements in simple algebraic groups of type.

This is formalized by the field with one element, which considers Coxeter groups to be simple algebraic groups over the field with one element. Glossary of algebraic groups. There are a number of mathematical notions to study and classify algebraic groups. In the sequel, G denotes an algebraic group over a field k. Bala P., Carter R. W., Classes of unipotent elements in simple algebraic groups I, Math. Proc. Cambridge Phi. Soc., 79, , p. – Google Scholar.

Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share . The centralizer of an element of a group is not abelian in general; C (a) means the largest subgroup of G which its element commutes with a fixed element a. If a is an element of center then C (a) = G. So as a counterexample, set G = S 3 and a = 1 is fine.

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### Centres of centralizers of unipotent elements in simple algebraic groups by R. Lawther Download PDF EPUB FB2

Centres of centralizers of unipotent elements in simple algebraic groups About this Title. Lawther and D.M. Testerman. Publication: Memoirs of the American Mathematical Society Publication Year: ; VolumeNumber ISBNs: (print); (online).

Let $$G$$ be a simple algebraic group defined over an algebraically closed field $$k$$ whose characteristic is either $$0$$ or a good prime for $$G$$, and let $$u\in G$$ be unipotent. The authors study the centralizer $$C_G(u)$$, especially its centre $$Z(C_G(u))$$.

Get this from a library. Centres of centralizers of unipotent elements in simple algebraic groups. [R Lawther; Donna M Testerman]. Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups R.

Lawther D. Testerman. Contents 1. Introduction 1 2. Notationandpreliminaryresults 5 3. Reductionoftheproblem 10 4. Classicalgroups 14 Let G be a simple algebraic group deﬁned over an algebraically closed ﬁeld k. Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups Article in Memoirs of the American Mathematical Society () March with 28 Reads How we measure 'reads'.

Centres of centralizers of unipotent elements in simple algebraic groups Testerman, Donna ; Lawther, Ross Let G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let u is an element of G be unipotent.

Centers of Centralizers of Unipotent Elements in Exceptional Algebraic Groups. THIS IS A TEMPORARY TITLE AGEP It will be replaced for the nal print by. This book concerns the theory of unipotent elements in simple algebraic groups part of the centralizer is embedded in the ambient group.

The book is divided into 22 chapters. The rst is an introduction to the topic Component groups of centralizers of unipotent elements in semisimple algebraic groups, Akad.

Nauk Gruzin. SSR Trudy Tbiliss. The dimensions of double centralizers of unipotent elements in these groups are unknown. Representatives. In this section we give our choice of representatives for unipotent classes in a simple algebraic group G of type E 7 or E 8.

The E 7 representatives in the tables of this section can be read off from the E 8 representatives. We give the. Classes of unipotent elements in simple algebraic groups. II - Volume 80 Issue 1 - P. Bala, R. Carter. Let G be a semisimple algebraic group defined over an algebraically closed field K of good characteristic p > u be a unipotent element of G of order p t, for some t ∈ N.

In this paper it is shown that u lies in a closed subgroup of G isomorphic to the it Witt group W t (K), which is a t‐dimensional connected abelian unipotent algebraic group.

Mathematics Subject. This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras.

The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. this book is the.

search topics focusing on the unipotent elements of a connected re-ductive algebraic group G, over an algebraically closed eld k, and nilpotent elements in the Lie algebra g = LieG.

The rst topic is a determination of canonical forms for unipotent classes and. Get this from a library. Centres of centralizers of unipotent elements in simple algebraic groups.

[Ross Lawther; Donna M Testerman]. The book provides a useful exposition of results on the structure of semisimple algebraic groups over an arbitrary algebraically closed field.

After the fundamental work of Borel and Chevalley in the s and s, further results were obtained over the next thirty years on conjugacy classes and centralizers of elements of such groups.

algebraic group and its Lie algebra have intrinsically de ned semisimple and unipotent (or nilpotent) elements which propagate naturally under mor-phisms. We begin with an algebraic group G over an algebraically closed eld K of characteristic p 0, together with its Lie algebra g. But the ideas mostly.

[Som98] describing the component groups of unipotent (or nilpotent) centralizers. We recall a few deﬁnitions before stating the main result. A pseudo-Levi subgroup Lof Gis the connected centralizer Co G (s) of a semisim-ple element s2G. The reductive group Lcontains a maximal torus Tof G, and.

Let G be a simple algebraic group deﬁned over an algebraically closed ﬁeld of characteristic p, and u ∈G be a non-regular unipotent element. Then either (i) CG(u) is non-abelian;or (ii) G =G2,p=3and u is a subregular unipotent element, in which case CG(u) is a 4-dimensional abelian unipotent group, but CG(u)is non-abelian.

We study the unipotent elements of disconnected algebraic groups of the form G, where G is a simple algebraic group in characteristic p possessing a graph automorphism tau of order p. Conjugacy Classes in Semisimple Algebraic Groups James E.

Humphreys After the fundamental work of Borel and Chevalley in the s and s on the structure and classification of semisimple algebraic groups over an arbitrary algebraically closed field, further results were obtained on conjugacy classes and centralizers.

Algebra and Algebraic Geometry Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups R. Lawther, Girton College, University of Cambridge, England, and D. M. Testerman, École Polytechnique Federale de Lausanne, Switzerland Contents: Introduction; Notation and preliminary results; Reduction of the problem; Classical groups.This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras.

The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. this book is the first.On Richardson classes of unipotent elements in semisimple algebraic groups Hirai, Takeshi, Proceedings of the Japan Academy, Series A, Mathematical Sciences, ; On the automorphism group of a semisimple Jordan algebra of characteristic zero Gordon, S.

Robert, Bulletin of the American Mathematical Society,