On pre-Novikov algebras and derived Zinbiel variety
| Autor: | Kolesnikov, P. S., Mashurov, F. A., Sartayev, B. K. |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2305.07371 |
| Popis: | For a non-associative algebra $A$ with a derivation $d$, its derived algebra $A^{(d)}$ is the same space equipped with new operations $a\succ b = d(a)b$, $a\prec b = ad(b)$, $a,b\in A$. 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 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. Comment: 12 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|