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Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

2011 Mathematics
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Release : 2011
Genre : Mathematics
Kind : eBook
Book Rating : 694/5 ( reviews)

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Book Synopsis Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups by : Ross Lawther

Download or read book Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups written by Ross Lawther. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: 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 uEG be unipotent. The authors study the centralizer CG(u), especially its centre Z(CG(u)). They calculate the Lie algebra of Z(CG(u)), in particular determining its dimension; they prove a succession of theorems of increasing generality, the last of which provides a formula for dim Z(CG(u)) in terms of the labelled diagram associated to the conjugacy class containing u.

Centers of Centralizers of Unipotent Elements in Exceptional Algebraic Groups

2013
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Release : 2013
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Kind : eBook
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Book Synopsis Centers of Centralizers of Unipotent Elements in Exceptional Algebraic Groups by : Iulian Ion Simion

Download or read book Centers of Centralizers of Unipotent Elements in Exceptional Algebraic Groups written by Iulian Ion Simion. This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt:

Groups of Exceptional Type, Coxeter Groups and Related Geometries

2014-04-02 Mathematics
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Release : 2014-04-02
Genre : Mathematics
Kind : eBook
Book Rating : 140/5 ( reviews)

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Book Synopsis Groups of Exceptional Type, Coxeter Groups and Related Geometries by : N.S. Narasimha Sastry

Download or read book Groups of Exceptional Type, Coxeter Groups and Related Geometries written by N.S. Narasimha Sastry. This book was released on 2014-04-02. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation.

Lie Theory

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 922/5 ( reviews)

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Book Synopsis Lie Theory by : Jean-Philippe Anker

Download or read book Lie Theory written by Jean-Philippe Anker. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: * First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.

Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras

2012-01-25 Mathematics
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Release : 2012-01-25
Genre : Mathematics
Kind : eBook
Book Rating : 205/5 ( reviews)

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Book Synopsis Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras by : Martin W. Liebeck

Download or read book Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras written by Martin W. Liebeck. This book was released on 2012-01-25. Available in PDF, EPUB and Kindle. Book excerpt: 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. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.

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