Module Hom-algebras

TL;DR

This paper introduces module Hom-algebras, a twisted deformation of module algebras, demonstrating their formation via endomorphisms and providing examples with q-deformations of sl(2) actions.

Contribution

It presents the concept of module Hom-algebras and shows how they can be derived from module algebras through endomorphisms, including explicit q-deformation examples.

Findings

Module Hom-algebras are deformations of module algebras via endomorphisms.

Constructed q-deformations of sl(2) actions on the affine plane.

Established a framework for twisted algebraic structures.

Abstract

We study a twisted version of module algebras called module Hom-algebras. It is shown that module algebras deform into module Hom-algebras via endomorphisms. As an example, we construct certain q-deformations of the usual sl(2)-action on the affine plane.