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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212106 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| Summary: | 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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| ISSN: | 1815-0659 |