Higher derived brackets, strong homotopy associative algebras and Loday pairs

TL;DR

This paper introduces a new method for constructing strong homotopy associative algebras using higher derived products, and extends the concept to noncommutative Loday pairs, enriching the theory of homotopy algebraic structures.

Contribution

It presents a novel higher derived product construction for strong homotopy associative algebras and introduces Loday pairs as a noncommutative analogue of Leibniz pairs.

Findings

Developed a quick method for higher derived product construction

Introduced the concept of Loday pairs as noncommutative Leibniz pairs

Studied strong homotopy Loday pairs and their higher derived brackets

Abstract

We give a quick method of constructing strong homotopy associative algebra, namely, the higher derived product construction. This method is associative analogue of classical higher derived bracket construction in the category of Loday algebras. We introduce a new type of algebra "Loday pair" which is noncommutative analogue of classical Leibniz pair. We study strong homotopy Loday pairs and the higher derived brackets on the Loday pairs.