کلاس‌های یگانه و ناپایدار در گروه‌های جبری ساده و جبرهای لی

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 Cover 1 Title page 4 Contents 8 Preface 12 Introduction 14 Preliminaries 22 Classical groups in good characteristic 52 Classical groups in bad characteristic: Statement of results 72 Nilpotent elements: The symplectic and orthogonal cases, p=2 78 Unipotent elements in symplectic and orthogonal groups, p=2 104 Finite classical groups 126 Tables of examples in low dimensions 132 Exceptional groups: Statement of results for nilpotent elements 142 Parabolic subgroups and labellings 146 Reductive subgroups 152 Annihilator spaces of nilpotent elements 166 Standard distinguished nilpotent elements 182 Exceptional distinguished nilpotent elements 216 Nilpotent classes and centralizers in E8 232 Nilpotent elements in the other exceptional types 276 Exceptional groups: Statement of results for unipotent elements 294 Corresponding unipotent and nilpotent elements 300 Distinguished unipotent elements 312 Non-distinguished unipotent classes 330 Proofs of theorems 1, 2 and corollaries 3– 354 Tables of nilpotent and unipotent classes in the exceptional groups 364 Bibliography 386 Glossary of symbols 390 Index 392 Back Cover 394 "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"--Site web de l'éditeur "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"--Pub. website