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Extending Structures : Fundamentals and Applications.
・ISBN 978-0-8153-4784-2 hard GB£ 187.99
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電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-1-351-16872-4
| 著者・編者 | Agore, Ana / Militaru, Gigel, |
|---|---|
| シリーズ | Chapman & Hall/CRC Monographs and Research Notes in Mathematics |
| 出版社 | (CRC Press Inc, US) |
| 出版年月 | 2019 |
| ページ数 | 242 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-7577＞ |
解説
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