# Deformations of Loday-type algebras and their morphisms

## TL;DR

This paper explores formal deformations of Loday-type algebras and their morphisms, extending Gerstenhaber's deformation theory to a broader class of algebraic structures and providing explicit cohomology descriptions.

## Contribution

It introduces a deformation framework for Loday-type algebras, including their morphisms, and explicitly characterizes their cohomology with coefficients in a representation.

## Key findings

- Cohomology of Loday-type algebras explicitly described
- Deformation theory extended to twisted Loday analogs
- Morphisms between Loday-type algebras also deformable

## Abstract

We study formal deformations of multiplication in an operad. This closely resembles Gerstenhaber's deformation theory for associative algebras. However, this applies to various algebras of Loday-type and their twisted analogs. We explicitly describe the cohomology of these algebras with coefficients in a representation. Finally, deformation of morphisms between algebras of the same Loday-type is also considered.