Contents
Preface xv
Chapter 1. Introduction 1
§1.1. Basic Definitions 1
§1.2. Simple Lie Superalgebras 3
§1.3. Classification of Classical Simple Lie Superalgebras 8
§1.4. Exercises 9
Chapter 2. The Classical Simple Lie Superalgebras. I 11
§2.1. Introduction 11
§2.2. Lie Superalgebras of Type A(m,n) 12
§2.3. The Orthosymplectic Lie Superalgebras 14
2.3.1. The Lie Superalgebras
osp(2m
+ 1, 2n) 15
2.3.2. The Lie Superalgebras
osp(2m,
2n) 16
2.3.3. The Lie Superalgebras
osp(2,
2n 2) 16
§2.4. The Strange Lie Superalgebras
p(n)
and
q(n)
17
2.4.1. The Lie Superalgebras
p(n)
17
2.4.2. The Lie Superalgebras
q(n)
17
§2.5. Rationality Issues 19
§2.6. The Killing Form 19
§2.7. Exercises 20
Chapter 3. Borel Subalgebras and Dynkin-Kac Diagrams 25
§3.1. Introduction 25
§3.2. Cartan Subalgebras and Borel-Penkov-Serganova
Subalgebras 28
vii
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