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Polyadic Groups.
・ISBN 978-1-032-69724-6 hard GB£ 145.99
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電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-1-032-70354-1
| 著者・編者 | Dudek, Wieslaw A., |
|---|---|
| 出版社 | (Chapman & Hall/CRC, UK) |
| 出版年月 | 2024 |
| ページ数 | 408 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-1303 M25-1931＞ |
解説
This book provides a general, unified approach to the theory of polyadic groups, their normal subgroups and matrix representations.
The author focuses on those properties of polyadic groups which are not present in the binary case. These properties indicate a strong relationship between polyadic groups and various group-like algebras, as well as ternary Hopf algebras and n-Lie algebras that are widely used in theoretical physics.
The relationships of polyadic groups with special types of binary groups, called covering groups and binary retracts, are described. These relationships allow the study of polyadic groups using these binary groups and their automorphisms.
The book also describes the affine geometry induced by polyadic groups and fuzzy subsets defined on polyadic groups. Finally, we discuss the categories of polyadic groups and the relationships between the different varieties of polyadic groups. In many cases, we give elegant new proofs of known theorems. We also give many interesting examples and applications.
The book contains many little-known results from articles previously published in hard-to-reach Russian, Ukrainian and Macedonian journals. These articles are not in English.