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Foreword

Abdenacer MAKHLOUF

IRIMAS-Department of Mathematics, University of Haute Alsace, Mulhouse, France

We set out to compile several volumes pertaining to Algebra and Applications in order to present new research trends in algebra and related topics. The subject of algebra has grown spectacularly over the last several decades; algebra reasoning and combinatorial aspects turn out to be very efficient in solving various problems in different domains. Our objective is to provide an insight into the fast development of new concepts and theories. The chapters encompass surveys of basic theories on non-associative algebras, such as Jordan and Lie theories, using modern tools in addition to more recent algebraic structures, such as Hopf algebras, which are related to quantum groups and mathematical physics.

We provide self-contained chapters on various topics in algebra, each combining some of the features of both a graduate-level textbook and a research-level survey. They include an introduction with motivations and historical remarks, the basic concepts, main results and perspectives. Furthermore, the authors provide comments on the relevance of the results, as well as relations to other results and applications.

This first volume deals with non-associative and graded algebras (Jordan algebras, Lie theory, composition algebras, division algebras, pre-Lie algebras, Krichever–Novikov type algebras, C*-algebras and H*-algebras) and provides an introduction to derived categories.

I would like to express my deep gratitude to all the contributors of this volume and ISTE Ltd for their support.