On Pre-Novikov Algebras and Derived Zinbiel Variety Full article
| Journal |
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
ISSN: 1815-0659 |
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| Output data | Year: 2024, Volume: 20, Article number : 017, Pages count : 15 DOI: 10.3842/sigma.2024.017 | ||||||||
| Tags | Novikov algebra; derivation; dendriform algebra; Zinbiel algebra | ||||||||
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
Abstract:
For a non-associative algebra A with a derivation d, its derived algebra A(d) is the same space equipped with new operations a ≻ b = d(a)b, a ≺ b = ad(b), a,b ∈ A. Given a variety Var of algebras, its derived variety is generated by all derived algebras A(d) for all A in Var and for all derivations d of A. 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.
Cite:
Kolesnikov P.
, Mashurov F.
, Sartayev B.
On Pre-Novikov Algebras and Derived Zinbiel Variety
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2024. V.20. 017 :1-15. DOI: 10.3842/sigma.2024.017 WOS Scopus РИНЦ OpenAlex
On Pre-Novikov Algebras and Derived Zinbiel Variety
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2024. V.20. 017 :1-15. DOI: 10.3842/sigma.2024.017 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Aug 31, 2023 |
| Published online: | Feb 28, 2024 |
| Published print: | Apr 1, 2024 |
Identifiers:
| Web of science: | WOS:001177272600001 |
| Scopus: | 2-s2.0-85186423629 |
| Elibrary: | 66209073 |
| OpenAlex: | W4392238341 |