Algebra and Applications 1 Non associative Algebras and Categories 1st Edition by Abdenacer Makhlouf ISBN 9781789450170 1789450179

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ISBN 10: 1789450179
ISBN 13: 9781789450170
Author: Abdenacer Makhlouf

Algebra and Applications 1 Non associative Algebras and Categories 1st Edition Table of contents:

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

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

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

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

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

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

7 An Introduction to Pre-Lie Algebras

7.1 Introduction

7.2 Some appearances of pre-Lie algebras

7.3 Some basic results and constructions of pre-Lie algebras

7.4 Pre-Lie algebras and CYBE

7.5 A larger framework: Lie analogues of Loday algebras

7.6 References

8 Symplectic, Product and Complex Structures on 3-Lie Algebras

8.1 Introduction

8.2 Preliminaries

8.3 Representations of 3-pre-Lie algebras

8.4 Symplectic structures and phase spaces of 3-Lie algebras

8.5 Product structures on 3-Lie algebras

8.6 Complex structures on 3-Lie algebras

8.7 Complex product structures on 3-Lie algebras

8.8 Para-Kähler structures on 3-Lie algebras

8.9 Pseudo-Kähler structures on 3-Lie algebras

8.10 References

9 Derived Categories

9.1 Introduction

9.2 Grothendieck’s definition

9.3 Verdier’s definition

9.4 Triangulated structure

9.5 Derived functors

9.6 Derived Morita theory

9.7 Dg categories

9.8 References

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Tags: Abdenacer Makhlouf, Applications, Non associative, Categories