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.

This book is part of Algebra and Geometry, a subject within theSCIENCES collection published by ISTE and Wiley, and the first of threevolumes specifically focusing on algebra and its applications. Algebraand Applications 1 centers on non-associative algebras and includes anintroduction to derived categories. The chapters are written byrecognized experts in the field, providing insight into new trends, as wellas a comprehensive introduction to the theory.The book incorporatesself-contained surveys with the main results, applications andperspectives.The chapters in this volume cover a wide variety of algebraic structuresand their related topics. Jordan superalgebras, Lie algebrascomposition algebras, graded division algebras, non-associative C*algebras, H*-algebras, Krichever-Novikov type algebras, preLie algebrasand related structures, geometric structures on 3-Lie algebras andderived categories are all explored.Algebra and Applications 1 is of great interest to graduate students andresearchers.Each chapter combines some of the features of both agraduate level textbook and of research level surveys.

Foreword xiAbdenacer MAKHLOUFChapter 1. Jordan Superalgebras 1Consuelo MARTINEZ and Efim ZELMANOVChapter 2. Composition Algebras 27Alberto ELDUQUEChapter 3. Graded-Division Algebras 59Yuri BAHTURIN, Mikhail KOCHETOV and Mikhail ZAICEVChapter 4. Non-associative C¯*-algebras 111Ángel RODRÍGUEZ PALACIOS and Miguel CABRERA GARCÍAChapter 5. Structure of H¯*-algebras 155José Antonio CUENCA MIRAChapter 6. Krichever-Novikov Type Algebras: Definitions and Results 199Martin SCHLICHENMAIERChapter 7. An Introduction to Pre-Lie Algebras 245Chengming BAIChapter 8. Symplectic, Product and Complex Structures on 3-Lie Algebras 275Yunhe SHENG and Rong TANGChapter 9. Derived Categories 321Bernhard KELLERList of Authors 347Index 349