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.
Lie Groups and Algebraic Groups
Lie Groups and 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 Lie Groups and Algebraic Groups write by Arkadij L. Onishchik. This book was released on 2012-12-06. Lie Groups and Algebraic Groups available in PDF, EPUB and Kindle. This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents.
Conjugacy Classes in Semisimple Algebraic Groups
Conjugacy Classes in Semisimple 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 Conjugacy Classes in Semisimple Algebraic Groups write by James E. Humphreys. This book was released on 1995. Conjugacy Classes in Semisimple Algebraic Groups available in PDF, EPUB and Kindle. 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 1950s and 1960s, further results were obtained over the next thirty years on conjugacy classes and centralizers of elements of such groups.
Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups
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.
Representations and Nilpotent Orbits of Lie Algebraic Systems
Representations and Nilpotent Orbits of Lie Algebraic Systems - 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 Representations and Nilpotent Orbits of Lie Algebraic Systems write by Maria Gorelik. This book was released on 2019-10-18. Representations and Nilpotent Orbits of Lie Algebraic Systems available in PDF, EPUB and Kindle. This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.
