Leibniz Algebras: Structure and Classification

Leibniz Algebras: Structure and Classification is a book that provides an introduction to the theory of Leibniz algebras, which are a generalization of Lie algebras. It covers important and more general parts of the structural theory of Leibniz algebras that are not addressed in other texts, and proposes a method of classification of a subclass of Leibniz algebras based on algebraic invariants. The book is suitable for final year bachelor's students, master's students, and PhD students going into research in the structural theory of finite-dimensional algebras, particularly Lie and Leibniz algebras.

Format: Paperback / softback
Length: 324 pages
Publication date: 13 June 2022
Publisher: Taylor & Francis Ltd

Leibniz Algebras: Structure and Classification is a comprehensive guide designed to introduce readers to the fascinating realm of Leibniz algebras. These algebras, a generalization of Lie algebras, possess a remarkable characteristic: the right multiplication operators act as derivations. This property sets them apart and was first explored by A.M. Blokh in the 1960s under the name D-algebras, highlighting their close connection with derivations. While the theory of D-algebras initially received less attention than it deserved, it was later reintroduced by Jean-Louis Loday in 1993, earning them the name Leibniz algebras due to their satisfying identity. The primary motivation behind the introduction of Leibniz algebras was to delve into the study of periodicity phenomena in algebraic K-theory.

In the modern era of algebra, the theory of Leibniz algebras stands as one of the most actively evolving fields. Alongside remarkable (co)homological, structural, and classification results, there has been a growing emergence of papers exploring various applications of Leibniz algebras. However, the primary focus of this book remains centered on the classification challenges of Leibniz algebras. Specifically, the authors present a method for classifying a subclass of Leibniz algebras based on algebraic invariants. This method holds applicability even in the context of Lie algebras.

Key Features:
• Provides a systematic and comprehensive exposition of the theory of Leibniz algebras and recent advancements in this field.
• Suitable for final-year bachelor's students, master's students, and Ph.D. students embarking on research in the structural theory of finite-dimensional algebras, particularly Lie and Leibniz algebras.
• Covers essential and more general aspects of the structural theory of Leibniz algebras that are not addressed in other textbooks.

In summary, Leibniz Algebras: Structure and Classification is an indispensable resource for anyone seeking to delve into the world of Leibniz algebras. With its systematic presentation, comprehensive coverage, and application to classification problems, this book, is a valuable tool for students, researchers, and enthusiasts alike.

Weight: 600g
Dimension: 234 x 156 (mm)
ISBN-13: 9781032337722