Hom-quantum groups III: Representations and module Hom-algebras

TL;DR

This paper explores the structure and representations of Hom-quantum groups, introducing new twisting principles and providing examples like Hom-quantum spaces and modules, advancing the understanding of Hom-type algebraic systems.

Contribution

It formulates two Twisting Principles for Hom-type algebras and constructs various Hom-quantum algebra examples, expanding the theoretical framework and applications.

Findings

Established two Twisting Principles for Hom-algebras

Constructed Hom-quantum n-spaces and enveloping algebras

Developed Hom-Verma modules and Hom-analogues of U_q(sl_2) structures

Abstract

We study Hom-quantum groups, their representations, and module Hom-algebras. Two Twisting Principles for Hom-type algebras are formulated, and construction results are proved following these Twisting Principles. Examples include Hom-quantum n-spaces, Hom-quantum enveloping algebras of Kac-Moody algebras, Hom-Verma modules, and Hom-type analogs of U_q(sl_2)-module-algebra structures on the quantum planes.