Author(s): Yuri A. Bahturin, Alexander A. Mikhalev, Viktor M. Petrogradsky, Mikhail V. Zaicev
Series: de Gruyter Expositions in Mathematics #7
Year: 1992
Preface vii
List of Symbols ix
Chapter 1
Basic facts about Lie superalgebras
§ 0. Some background 1
§ 1. Graded algebras 4
§ 2. Identical relations of graded algebras 22
Exercises 35
Comments to Chapter 1 37
Chapter 2
The structure of free Lie superalgebras
§ 1. The free colour Lie superalgebra, s-regular words and
monomials 39
§ 2. Bases of free colour Lie superalgebras 44
§3. The freeness of subalgebras and its corollaries 53
§ 4. Bases and subalgebras of free colour Lie p-superalgebras 69
§ 5. The lattice of finitely generated subalgebras 75
§ 6. Free colour Lie super-rings 78
Comments to Chapter 2 80
Chapter 3
Composition techniques in the theory of Lie superalgebras
§1. The Diamond Lemma for associative rings 81
§ 2. Universal enveloping algebras 84
§ 3. The Composition Lemma 95
§4. Free products with amalgamated subalgebra 105
Comments to Chapter 3 108
Chapter 4
Identities in enveloping algebras
§1. Main results 111
§2. Delta-sets 123
§ 3. Identities in enveloping algebras of nilpotent Lie superalgebras 129
§4. The case of characteristic zero 136
Comments to Chapter 4 144
Chapter 5
Irreducible representations of Lie superalgebras
§ 1. The Jacobson radical of universal enveloping algebras 147
§2. Dimensions of irreducible representations 152
§ 3. More on restricted enveloping algebras 160
§4. Examples 171
Comments to Chapter 5 173
Chapter 6
Finiteness conditions for colour Lie superalgebras
with identities
§ 1. Various types of finiteness conditions. Examples 175
§2. Maximal condition and Hopf property 180
§ 3. Sufficient conditions for residual finiteness 201
§4. Representability of Lie superalgebras by matrices 210
Comments to Chapter 6 236
Bibliography 237
Author Index 247
Subject Index 249
