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, pre Lie 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.
Spis treści
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
O autorze
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.
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