Extending Structures: Fundamentals and Applications

1st Edition

Ana Agore, Gigel Militaru

CRC Press
Published August 27, 2019
Reference - 224 Pages
ISBN 9780815347842 - CAT# K345489
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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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.


  • 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