Lie-admissible, Associative-admissible Operads and Non-symmetric Versions of Symmetric Operads

Authors

  • Askar S. Dzhumadil'daev Institute of Mathematics and Mathematical Modeling, Kazakhstan

DOI:

https://doi.org/10.7546/CRABS.2024.11.01

Keywords:

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

Abstract

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 $$\pm$$-Jacobi admissible and $$\pm$$-associative-admissible if it satisfies the Jacobi identity and the associative identity under $$\pm$$-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.

Author Biography

Askar S. Dzhumadil'daev, Institute of Mathematics and Mathematical Modeling, Kazakhstan

Mailing Address:
Institute of Mathematics and Mathematical Modeling,
Almaty, Kazakhstan

E-mail: dzhuma@hotmail.com

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Published

30-11-2024

How to Cite

[1]
A. Dzhumadil’daev, “Lie-admissible, Associative-admissible Operads and Non-symmetric Versions of Symmetric Operads”, C. R. Acad. Bulg. Sci., vol. 77, no. 11, pp. 1577–1588, Nov. 2024.

Issue

Section

Mathematics