Simultaneous deformations of algebras and morphisms via derived brackets

TL;DR

This paper introduces a new explicit method using derived brackets to study simultaneous deformations of algebraic structures and their morphisms, offering an alternative to traditional operad-based approaches.

Contribution

The authors develop an explicit construction of L-infinity algebras for simultaneous deformations, bypassing complex operad machinery.

Findings

Provides a practical method for constructing deformation algebras

Simplifies the process compared to operad-based techniques

Enables explicit calculations of deformations

Abstract

We present a method to construct explicitly L-infinity algebras governing simultaneous deformations of various kinds of algebraic structures and of their morphisms. It is an alternative to the heavy use of the operad machinery of the existing approaches. Our method relies on Voronov's derived bracket construction.