Algebra and Applications 1

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.

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

Abdenacer Makhlouf is a Professor and head of the mathematics department at the University of Haute Alsace, France. His research covers structure, representation theory, deformation theory and cohomology of various types of algebras, including non-associative algebras, Hopf algebras and n-ary algebras.