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.
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.
Table of Contents
Foreword xi
Abdenacer MAKHLOUF
Chapter 1. Jordan Superalgebras 1
Consuelo MARTINEZ and Efim ZELMANOV
Chapter 2. Composition Algebras 27
Alberto ELDUQUE
Chapter 3. Graded-Division Algebras 59
Yuri BAHTURIN, Mikhail KOCHETOV and Mikhail ZAICEV
Chapter 4. Non-associative C∗-algebras 111
Ángel RODRÍGUEZ PALACIOS and Miguel CABRERA GARCÍA
Chapter 5. Structure of H∗-algebras 155
José Antonio CUENCA MIRA
Chapter 6. Krichever-Novikov Type Algebras: Definitions and Results 199
Martin SCHLICHENMAIER
Chapter 7. An Introduction to Pre-Lie Algebras 245
Chengming BAI
Chapter 8. Symplectic, Product and Complex Structures on 3-Lie Algebras 275
Yunhe SHENG and Rong TANG
Chapter 9. Derived Categories 321
Bernhard KELLER
List of Authors 347
Index 349
