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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. 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
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