Extending Structures: Fundamentals and Applications

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Ana Agore (Vrije Universiteit Brussel, Belgium) Gigel Militaru (University of Bucharest, Faculty of Mathematics and Computer Science, Romania)

Extending Structures

Fundamentals and Applications

Ana Agore (Vrije Universiteit Brussel, Belgium), Gigel Militaru (University of Bucharest, Faculty of Mathematics and Computer Science, Romania)

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English

CRC Press Inc
27 August 2019

Algebra; Groups & group theory; Applied mathematics

Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Extending Structures: Fundamentals and Applications treats the extending structures (ES) problem in the context of groups, Lie/Leibniz algebras, associative algebras and Poisson/Jacobi algebras. This concisely written monograph offers the reader an incursion into the extending structures problem which provides a common ground for studying both the extension problem and the factorization problem.

Features

Provides a unified approach to the extension problem and the factorization problem

Introduces the classifying complements problem as a sort of converse of the factorization problem; and in the case of groups it leads to a theoretical formula for computing the number of types of isomorphisms of all groups of finite order that arise from a minimal set of data

Describes a way of classifying a certain class of finite Lie/Leibniz/Poisson/Jacobi/associative algebras etc. using flag structures

Introduces new (non)abelian cohomological objects for all of the aforementioned categories

As an application to the approach used for dealing with the classification part of the ES problem, the Galois groups associated with extensions of Lie algebras and associative algebras are described

By: Ana Agore (Vrije Universiteit Brussel Belgium), Gigel Militaru (University of Bucharest, Faculty of Mathematics and Computer Science, Romania)
Imprint: CRC Press Inc
Country of Publication: United States
Dimensions: Height: 234mm, Width: 156mm,
Weight: 480g
ISBN: 9780815347842
ISBN 10: 0815347847
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Pages: 242
Publication Date: 27 August 2019
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Active

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

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.

Reviews for Extending Structures: Fundamentals and Applications

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