Extending Structures

Fundamentals and Applications
1. Auflage 2019
ISBN: 978-0-8153-4784-2
Verlag: CRC Press

Buch, Englisch, 242 Seiten, Format (B × H): 160 mm x 239 mm, Gewicht: 499 g

Reihe: 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

Autoren/Hrsg.

Agore, Ana

Militaru, Gigel

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

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

Über Autor(innen)

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.