Isomorphism Criteria for A Subclass of Filiform Leibniz Algebras
In the paper, we propose three isomorphism criteria for a subclass of finite-dimensional Leibniz algebras. Isomorphism Criterion 1 has been given earlier (see [5]). We introduce notations for new structure constants. Using the new notation, we state the isomorphism criterion 2. To formulate Isomorph...
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| Language: | English |
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Horizon Research Publishing
2023
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| Online Access: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85162187213&doi=10.13189%2fms.2023.110318&partnerID=40&md5=9c215ec7085c4f2643480321d87556cf |
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2-s2.0-85162187213 Rakhimov I.S. Isomorphism Criteria for A Subclass of Filiform Leibniz Algebras 2023 Mathematics and Statistics 11 3 10.13189/ms.2023.110318 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85162187213&doi=10.13189%2fms.2023.110318&partnerID=40&md5=9c215ec7085c4f2643480321d87556cf In the paper, we propose three isomorphism criteria for a subclass of finite-dimensional Leibniz algebras. Isomorphism Criterion 1 has been given earlier (see [5]). We introduce notations for new structure constants. Using the new notation, we state the isomorphism criterion 2. To formulate Isomorphism Criterion 3, we introduce “semi-invariant functions” needed. We prove that these three Isomorphism Criteria are equivalent. The isomorphism criterion 3 is convenient to find the invariant functions to represent isomorphism classes. The proof of the isomorphism criteria in the general case is computational and is based on hypothetic convolution identities given in [11]. Therefore, we give details in the ten-dimensional case. © 2023 by authors, all rights reserved. Horizon Research Publishing 23322071 English Article All Open Access; Gold Open Access |
| author |
Rakhimov I.S. |
| spellingShingle |
Rakhimov I.S. Isomorphism Criteria for A Subclass of Filiform Leibniz Algebras |
| author_facet |
Rakhimov I.S. |
| author_sort |
Rakhimov I.S. |
| title |
Isomorphism Criteria for A Subclass of Filiform Leibniz Algebras |
| title_short |
Isomorphism Criteria for A Subclass of Filiform Leibniz Algebras |
| title_full |
Isomorphism Criteria for A Subclass of Filiform Leibniz Algebras |
| title_fullStr |
Isomorphism Criteria for A Subclass of Filiform Leibniz Algebras |
| title_full_unstemmed |
Isomorphism Criteria for A Subclass of Filiform Leibniz Algebras |
| title_sort |
Isomorphism Criteria for A Subclass of Filiform Leibniz Algebras |
| publishDate |
2023 |
| container_title |
Mathematics and Statistics |
| container_volume |
11 |
| container_issue |
3 |
| doi_str_mv |
10.13189/ms.2023.110318 |
| url |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85162187213&doi=10.13189%2fms.2023.110318&partnerID=40&md5=9c215ec7085c4f2643480321d87556cf |
| description |
In the paper, we propose three isomorphism criteria for a subclass of finite-dimensional Leibniz algebras. Isomorphism Criterion 1 has been given earlier (see [5]). We introduce notations for new structure constants. Using the new notation, we state the isomorphism criterion 2. To formulate Isomorphism Criterion 3, we introduce “semi-invariant functions” needed. We prove that these three Isomorphism Criteria are equivalent. The isomorphism criterion 3 is convenient to find the invariant functions to represent isomorphism classes. The proof of the isomorphism criteria in the general case is computational and is based on hypothetic convolution identities given in [11]. Therefore, we give details in the ten-dimensional case. © 2023 by authors, all rights reserved. |
| publisher |
Horizon Research Publishing |
| issn |
23322071 |
| language |
English |
| format |
Article |
| accesstype |
All Open Access; Gold Open Access |
| record_format |
scopus |
| collection |
Scopus |
| _version_ |
1809677888353468416 |