On Pre-Novikov Algebras and Derived Zinbiel Variety

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Authors: Kolesnikov, Pavel, Mashurov, Farukh, Sartayev, Bauyrzhan
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212106
• 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

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...