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Table of Contents
1 Cover
4 Foreword
5 1 Jordan Superalgebras 1.1 Introduction 1.2 Tits–Kantor–Koecher construction 1.3 Basic examples (classical superalgebras) 1.4 Brackets 1.5 Cheng–Kac superalgebras 1.6 Finite dimensional simple Jordan superalgebras 1.7 Finite dimensional representations 1.8 Jordan superconformal algebras 1.9 References
6 2 Composition Algebras 2.1 Introduction 2.2 Quaternions and octonions 2.3 Unital composition algebras 2.4 Symmetric composition algebras 2.5 Triality 2.6 Concluding remarks 2.7 Acknowledgments 2.8 References
7 3 Graded-Division Algebras 3.1 Introduction 3.2 Background on gradings 3.3 Graded-division algebras over algebraically closed fields 3.4 Real graded-division associative algebras 3.5 Real loop algebras with a non-split centroid 3.6 Alternative algebras 3.7 Gradings of fields 3.8 References
8 4 Non-associative C*-algebras 4.1 Introduction 4.2 JB-algebras 4.3 The non-associative Vidav–Palmer and Gelfand–Naimark theorems 4.4 JB*-triples 4.5 Past, present and future of non-associative C*-algebras 4.6 Acknowledgments 4.7 References
9 5 Structure of H*-algebras 5.1 Introduction 5.2 Preliminaries: aspects of the general theory 5.3 Ultraproducts of H*-algebras 5.4 Quadratic H*-algebras 5.5 Associative H*-algebras 5.6 Flexible H*-algebras 5.7 Non-commutative Jordan H*-algebras 5.8 Jordan H*-algebras 5.9 Moufang H*-algebras 5.10 Lie H*-algebras 5.11 Topics closely related to Lie H*-algebras 5.12 Two-graded H*-algebras 5.13 Other topics: beyond the H*-algebras 5.14 Acknowledgments 5.15 References
10 6 Krichever–Novikov Type Algebras: Definitions and Results 6.1 Introduction 6.2 The Virasoro algebra and its relatives 6.3 The geometric picture 6.4 Algebraic structures 6.5 Almost-graded structure 6.6 Central extensions 6.7 Examples and generalizations 6.8 Lax operator algebras 6.9 Fermionic Fock space 6.10 Sugawara representation 6.11 Application to moduli space 6.12 Acknowledgments 6.13 References
