Algebra and Applications 1: Non-associative Algebras and Categories
- Length: 368 pages
- Edition: 1
- Language: English
- Publisher: Wiley-ISTE
- Publication Date: 2021-05-11
- ISBN-10: 1789450179
- ISBN-13: 9781789450170
- Sales Rank: #0 (See Top 100 Books)
This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the first of three volumes specifically focusing on algebra and its applications. Algebra and Applications 1 centers on non-associative algebras and includes an introduction to derived categories. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory.
The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Jordan superalgebras, Lie algebras, composition algebras, graded division algebras, non-associative C*- algebras, H*-algebras, Krichever-Novikov type algebras, preLie algebras and related structures, geometric structures on 3-Lie algebras and derived categories are all explored. Algebra and Applications 1 is of great interest to graduate students and researchers.
Each chapter combines some of the features of both a graduate level textbook and of research level surveys.
Cover Table of Contents Title Page Copyright Foreword 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 List of Authors Index End User License Agreement
Donate to keep this site alive
1. Disable the AdBlock plugin. Otherwise, you may not get any links.
2. Solve the CAPTCHA.
3. Click download link.
4. Lead to download server to download.