General Theory of Leibniz Algebras

“‘General Theory of Leibniz Algebras’ is a timely and significant contribution to modern algebra. It consolidates scattered results, advances the structural theory, and opens directions for future work. The book deserves a place in the library of every researcher working in the area of Leibniz algebra or more broadly in nonassociative algebra and will likely serve as a reference point for the development of the subject in the coming years.” (Ripan Saha, zbMATH 1573.17006, 2026)

This book discusses many interesting results have been obtained in Leibniz algebras over the past two decades. The authors not only summarize recent results and methods successfully used in Leibniz algebras, but also show new prospective horizons. Any mathematical theories have a number of natural problems that arise in the process of its development, and these problems quite often have analogues in other areas such as differential geometry, homological algebra, classical algebraic topology, noncommutative geometry, etc. With this in mind the authors describe the general structure of Leibniz algebras that have already been discovered. This approach allows readers to see which parts of the theory should be developed further and also shows the significant differences of Leibniz algebras from Lie algebras. Recent results that constitute the naturally evolving general theory of the subject are then explored.

In addition, this book:

• Summarizes results and methods used in Leibniz algebras and also shows new perspective horizons
• Discusses numerous interesting and promising results in the area of Leibniz algebras from the past two decades
• Addresses the significant differences of Leibniz algebras from Lie algebras