Extending structures – fundamentals and applications. (English) Zbl 1511.17001
Monographs and Research Notes in Mathematics. Boca Raton, FL: CRC Press (ISBN 978-0-8153-4784-2/hbk; 978-1-351-16872-4/ebook). xviii, 224 p. (2020).
Publisher’s description: The book 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:
Features:
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- Provides a unified approach to the extension problem and the factorization problem
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- 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
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- Describes a way of classifying a certain class of finite Lie/Leibniz/Poisson/Jacobi/associative algebras etc. using flag structures
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- Introduces new (non)abelian cohomological objects for all of the aforementioned categories
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- 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
MSC:
17-02 | Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras |
16-02 | Research exposition (monographs, survey articles) pertaining to associative rings and algebras |
16D20 | Bimodules in associative algebras |
16S70 | Extensions of associative rings by ideals |
17A32 | Leibniz algebras |
17B56 | Cohomology of Lie (super)algebras |
17B63 | Poisson algebras |
20E22 | Extensions, wreath products, and other compositions of groups |