On Pre-Novikov Algebras and Derived Zinbiel Variety
For a non-associative algebra with a derivation , its derived algebra ⁽ᵈ⁾ is the same space equipped with new operations ≻ = (), ≺ = (), , ∈ . Given a variety Var of algebras, its derived variety is generated by all derived algebras ⁽ᵈ⁾ for all in Var and for all derivations of . The same te...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212106 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On Pre-Novikov Algebras and Derived Zinbiel Variety. Pavel Kolesnikov, Farukh Mashurov and Bauyrzhan Sartayev. SIGMA 20 (2024), 017, 15 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862533149512171520 |
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| author | Kolesnikov, Pavel Mashurov, Farukh Sartayev, Bauyrzhan |
| author_facet | Kolesnikov, Pavel Mashurov, Farukh Sartayev, Bauyrzhan |
| citation_txt | On Pre-Novikov Algebras and Derived Zinbiel Variety. Pavel Kolesnikov, Farukh Mashurov and Bauyrzhan Sartayev. SIGMA 20 (2024), 017, 15 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For a non-associative algebra with a derivation , its derived algebra ⁽ᵈ⁾ is the same space equipped with new operations ≻ = (), ≺ = (), , ∈ . Given a variety Var of algebras, its derived variety is generated by all derived algebras ⁽ᵈ⁾ for all in Var and for all derivations of . The same terminology is applied to binary operads governing varieties of non-associative algebras. For example, the operad of Novikov algebras is the derived one for the operad of (associative) commutative algebras. We state a sufficient condition for every algebra from a derived variety to be embeddable into an appropriate differential algebra of the corresponding variety. We also find that for Var = Zinb, the variety of Zinbiel algebras, there exist algebras from the derived variety (which coincides with the class of pre-Novikov algebras) that cannot be embedded into a Zinbiel algebra with a derivation.
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| first_indexed | 2026-03-12T14:01:38Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212106 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-12T14:01:38Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kolesnikov, Pavel Mashurov, Farukh Sartayev, Bauyrzhan 2026-01-28T13:55:47Z 2024 On Pre-Novikov Algebras and Derived Zinbiel Variety. Pavel Kolesnikov, Farukh Mashurov and Bauyrzhan Sartayev. SIGMA 20 (2024), 017, 15 pages 1815-0659 2020 Mathematics Subject Classification: 17A36; 17A30; 18M60 arXiv:2305.07371 https://nasplib.isofts.kiev.ua/handle/123456789/212106 https://doi.org/10.3842/SIGMA.2024.017 For a non-associative algebra with a derivation , its derived algebra ⁽ᵈ⁾ is the same space equipped with new operations ≻ = (), ≺ = (), , ∈ . Given a variety Var of algebras, its derived variety is generated by all derived algebras ⁽ᵈ⁾ for all in Var and for all derivations of . The same terminology is applied to binary operads governing varieties of non-associative algebras. For example, the operad of Novikov algebras is the derived one for the operad of (associative) commutative algebras. We state a sufficient condition for every algebra from a derived variety to be embeddable into an appropriate differential algebra of the corresponding variety. We also find that for Var = Zinb, the variety of Zinbiel algebras, there exist algebras from the derived variety (which coincides with the class of pre-Novikov algebras) that cannot be embedded into a Zinbiel algebra with a derivation. F. Mashurov and B. Sartayev were supported by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP14870282). P. Kolesnikov was supported by the Program of Fundamental Research RAS (project FWNF-2022-0002). The authors are grateful to the referees for their useful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Pre-Novikov Algebras and Derived Zinbiel Variety Article published earlier |
| spellingShingle | On Pre-Novikov Algebras and Derived Zinbiel Variety Kolesnikov, Pavel Mashurov, Farukh Sartayev, Bauyrzhan |
| title | On Pre-Novikov Algebras and Derived Zinbiel Variety |
| title_full | On Pre-Novikov Algebras and Derived Zinbiel Variety |
| title_fullStr | On Pre-Novikov Algebras and Derived Zinbiel Variety |
| title_full_unstemmed | On Pre-Novikov Algebras and Derived Zinbiel Variety |
| title_short | On Pre-Novikov Algebras and Derived Zinbiel Variety |
| title_sort | on pre-novikov algebras and derived zinbiel variety |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212106 |
| work_keys_str_mv | AT kolesnikovpavel onprenovikovalgebrasandderivedzinbielvariety AT mashurovfarukh onprenovikovalgebrasandderivedzinbielvariety AT sartayevbauyrzhan onprenovikovalgebrasandderivedzinbielvariety |