Extending Structures

Ana Agore is a senior researcher at the Institute of Mathematics of the Romanian Academy, Romania. Her research interests include Hopf algebras and quantum groups, category theory and (non)associative algebras. Gigel Militaru is a professor at the University of Bucharest, Romania. His primary research interests are non commutative algebra, non-associative (Lie, Leibniz, Jacobi/Poisson) algebras, Hopf algebras and quantum groups.

"One of the most fundamental problems in all of abstract algebra is the question of building algebras using known subalgrebras. Agore (Romanian Academy) and Militaru (Univ. of Bucharest) present a unified theory of the many different approaches to the extension and classification problems in this jointly authored work. The text is extremely well written and well organized, with readers fully in mind. While it adds up to an excellent monograph that deserves to be added to any mathematics library, the book is essentially a compilation of professional papers by the authors, intended solely for researchers in this field. Even given this caveat, the professional mathematician might wonder if the book is right for their specific niche within extension theory. It is clear that the authors took this concern into consideration in crafting the table of contents. Each chapter forms its own module and focuses on one type of algebraic structure as it relates to the extension problem. Thus we have a chapter on groups, a chapter on associative algebras, a chapter on Lie algebras, and so on. Any interested researcher could pick up the book, flip to the chapter of interest and benefit from using this great reference."– Choice Review, A. Misseldine, Southern Utah University

• 1. Extending structures: the group case 2. Leibniz algebras 3.Lie algebras 4. Associative algebras 5. Jacobi and Poisson algebras.