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Algebra and Applications 1
Non-associative Algebras and Categories

Abdenacer Makhlouf (Author)

9781789450170, Wiley

Hardback, published 11 May 2021

368 pages
1 x 1 x 1 cm, 0.454 kg

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

Subject Areas: Mathematics [PB]
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