Extending Structures: Fundamentals and Applications
авг 2019. · CRC Press
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O ovoj e-knjizi
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
O autoru
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.
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