On a generalized Mizuhara construction Full article
| Journal |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2024, Volume: 65, Number: 3, Pages: 599–610 Pages count : DOI: 10.1134/S0037446624030091 | ||
| Tags | left-symmetric algebra, right-symmetric algebra, simple algebra, pre-Lie algebra, Mizuhara construction, endomorph, Burde algebra, Witt double | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
Abstract:
We describe the ideals for Mizuhara extensions and find some necessary and sufficient conditions for the simplicity of the direct Mizuhara extension. Also, we study the Mizuhara construction for the matrix algebra and Burde algebras. We construct some various generalizations of the Mizuhara construction and exhibit some examples of the simple pre-Lie algebras that are obtained by this construction; in particular, we construct the simple Witt doubles Ad and Wd(A ) for a unital associative commutative algebra A with derivation d.
Cite:
Pozhidaev A.P.
On a generalized Mizuhara construction
Siberian Mathematical Journal. 2024. V.65. N3. P.599–610. DOI: 10.1134/S0037446624030091 WOS Scopus РИНЦ OpenAlex
On a generalized Mizuhara construction
Siberian Mathematical Journal. 2024. V.65. N3. P.599–610. DOI: 10.1134/S0037446624030091 WOS Scopus РИНЦ OpenAlex
Original:
Пожидаев А.П.
Об обобщённой конструкции Мицухары
Сибирский математический журнал. 2024. Т.65. №3. С.545-559. DOI: 10.33048/smzh.2024.65.309 РИНЦ
Об обобщённой конструкции Мицухары
Сибирский математический журнал. 2024. Т.65. №3. С.545-559. DOI: 10.33048/smzh.2024.65.309 РИНЦ
Dates:
| Submitted: | Nov 9, 2023 |
| Accepted: | Apr 8, 2024 |
| Published print: | May 20, 2024 |
| Published online: | May 20, 2024 |
Identifiers:
| Web of science: | WOS:001235366000009 |
| Scopus: | 2-s2.0-85195149762 |
| Elibrary: | 67311446 |
| OpenAlex: | W4399142456 |