Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups write by Ross Lawther. This book was released on 2011. Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups available in PDF, EPUB and Kindle. 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.
Lie Theory
Lie Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie Theory write by Jean-Philippe Anker. This book was released on 2012-12-06. Lie Theory available in PDF, EPUB and Kindle. * 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.
Groups of Exceptional Type, Coxeter Groups and Related Geometries
Groups of Exceptional Type, Coxeter Groups and Related Geometries - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Groups of Exceptional Type, Coxeter Groups and Related Geometries write by N.S. Narasimha Sastry. This book was released on 2014-04-02. Groups of Exceptional Type, Coxeter Groups and Related Geometries available in PDF, EPUB and Kindle. 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.
Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras
Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras write by Martin W. Liebeck. This book was released on 2012-01-25. Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras available in PDF, EPUB and Kindle. 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.
On the Algebraic Foundations of Bounded Cohomology
On the Algebraic Foundations of Bounded Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On the Algebraic Foundations of Bounded Cohomology write by Theo Bühler. This book was released on 2011. On the Algebraic Foundations of Bounded Cohomology available in PDF, EPUB and Kindle. It is a widespread opinion among experts that (continuous) bounded cohomology cannot be interpreted as a derived functor and that triangulated methods break down. The author proves that this is wrong. He uses the formalism of exact categories and their derived categories in order to construct a classical derived functor on the category of Banach $G$-modules with values in Waelbroeck's abelian category. This gives us an axiomatic characterization of this theory for free, and it is a simple matter to reconstruct the classical semi-normed cohomology spaces out of Waelbroeck's category. The author proves that the derived categories of right bounded and of left bounded complexes of Banach $G$-modules are equivalent to the derived category of two abelian categories (one for each boundedness condition), a consequence of the theory of abstract truncation and hearts of $t$-structures. Moreover, he proves that the derived categories of Banach $G$-modules can be constructed as the homotopy categories of model structures on the categories of chain complexes of Banach $G$-modules, thus proving that the theory fits into yet another standard framework of homological and homotopical algebra.
