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Extending Structures: Fundamentals and Applications (Chapman & Hall/CRC Monographs and Research Notes in Mathematics) - Hardcover

Book 55 of 79: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Agore, Ana; Militaru, Gigel

 
9780815347842: Extending Structures: Fundamentals and Applications (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
Hardcover
ISBN 10: 0815347847 ISBN 13: 9780815347842
Publisher: CRC Press, 2019

Synopsis

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

"synopsis" may belong to another edition of this title.

About the Author

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.

"About this title" may belong to another edition of this title.

Publisher
CRC Press
Publication date
2019
Language
English
ISBN 10 
0815347847
ISBN 13 
9780815347842
Binding
Hardcover
Edition number
1
Number of pages
242