[PDF] Conjugacy Classes In Semisimple Algebraic Groups eBook
Conjugacy Classes In Semisimple Algebraic Groups Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Conjugacy Classes In Semisimple Algebraic Groups book. This book definitely worth reading, it is an incredibly well-written.
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.
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).
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.