LIE-ADMISSIBLE, ASSOCIATIVE-ADMISSIBLE OPERADS AND NON-SYMMETRIC VERSIONS OF SYMMETRIC OPERADS

Dzhumadil’daev A.S.
2024 Academic Publishing House

Comptes Rendus de LAcademie Bulgare des Sciences
2024 #77 Issue 11 1577 - 1588 pp.

A non-symmetric version of a symmetric operad is defined as the operad of algebras, where all consequences of the identity of degree 2 are valid in degree higher than 2 and not valid in degree 2. The main identity that should be included for such an operad is the reverse-associative identity a(bc) = (cb)a. An algebra is ±-Jacobi admissible and ±-associative-admissible if it satisfies the Jacobi identity and the associative identity under ±-commutators, respectively. In our paper we consider operads related to Lie-admissible, associative-admissible, and associative-Lie-admissible algebras. In particular we find the dimension sequences of their multilinear parts.

associative-admissible algebras , Koszul duality , Lie-admissible algebras , operads , polynomial identities

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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Institute of Mathematics and Mathematical Modeling

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