[PDF] Conjugacy Classes In Lie Algebras And Algebraic Groups eBook

Author : James E. Humphreys
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 50,7 MB
Release : 1995
Category : Education
ISBN : 0821852760

GET 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 1950s and 1960s, further results were obtained over the next thirty years on conjugacy classes and centralizers of elements of such groups.

Author : R. W Richardson (Jr)
Publisher :
Page : 22 pages
File Size : 11,53 MB
Release : 1966
Category :
ISBN :

GET BOOK

Kostant has shown that a complex semi-simple Lie algebra has only a finite number of nilpotent conjugacy classes. This paper shows how Kostant's theorem can be obtained as a special case of an elementary theorem on conjugacy classes in reductive subgroups of algebrais subgroups. As a corollary of this theorem we show that a semi-simple algebrais group over an algebraically closed field of characteristic p> 5 has only a finite number of unipotent conjugacy classes. Related conjugacy theorems are proved for subalgebras and homomorphisms of Lie algebras. (Author).

Author : Martin W. Liebeck
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 50,2 MB
Release : 2012-01-25
Category : Mathematics
ISBN : 0821869205

GET BOOK

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.

Author : Gus Lehrer
Publisher : Cambridge University Press
Page : 396 pages
File Size : 34,69 MB
Release : 1997-01-23
Category : Mathematics
ISBN : 9780521585323

GET BOOK

This volume contains original research articles by many of the world's leading researchers in algebraic and Lie groups. Its inclination is algebraic and geometic, although analytical aspects are included. The central theme reflects the interests of R. W. Richardson, viz connections between representation theory and the structure and geometry of algebraic groups. All workers on algebraic and Lie groups will find that this book contains a wealth of interesting material.

Author : B. Rosenfeld
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 44,6 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 147575325X

GET BOOK

This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.

Author : Roger W. Carter
Publisher :
Page : 570 pages
File Size : 30,8 MB
Release : 1993-08-24
Category : Mathematics
ISBN :

GET BOOK

The finite groups of Lie type are of basic importance in the theory of groups. A classic in its field, this book presents the theories of finite groups of Lie type in a clear and accessible style, especially with regard to the main concepts of the theory and the techniques of proof used, and gives a detailed exposition of the complex representation theory.

Author : Georgia Benkart
Publisher : American Mathematical Soc.
Page : 352 pages
File Size : 26,14 MB
Release : 1990
Category : Mathematics
ISBN : 0821851195

GET BOOK

Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.