4-type subvarieties of the variety of associative algebras

TL;DR

This paper explores four specific subvarieties within associative algebras, analyzing their operadic structures, relationships with known algebra classes, and identities involving commutator and anti-commutator operations.

Contribution

It introduces four new subvarieties of associative algebras, examines their operadic connections, and derives identities for their commutator and anti-commutator operations.

Findings

Identified four subvarieties of associative algebras

Connected these subvarieties with dendriform and Novikov algebras

Derived identities for commutator and anti-commutator operations

Abstract

In this paper, we consider four types of subvarieties of the variety of associative algebras. We study these subvarieties from the point of view of operads and show their connections with well-known classes of algebras, such as dendriform algebras and noncommutative Novikov algebras. Finally, we define the commutator and anti-commutator operations on these algebras and derive several identities satisfied by these operations.