Uniqueness and intrinsic properties of non-commutative Koszul brackets

TL;DR

This paper establishes the unique extension of higher Koszul brackets to all unitary associative algebras, linking square zero operators of degree 1 to curved L-infinity structures, revealing intrinsic properties of non-commutative Koszul brackets.

Contribution

It introduces a unique natural extension of Koszul brackets to associative algebras and connects square zero operators to curved L-infinity structures.

Findings

Existence of a unique extension of Koszul brackets.

Connection between square zero operators and curved L-infinity structures.

Intrinsic properties of non-commutative Koszul brackets.

Abstract

There exists a unique natural extension of higher Koszul brackets to every unitary associative algebras in a way that every square zero operator of degree 1 gives a curved L-infinity structure.