Quantum Drinfeld Orbifold Algebras

TL;DR

This paper generalizes conditions for quantum Drinfeld orbifold algebras, extending prior results on Drinfeld orbifold and quantum Drinfeld Hecke algebras, thus broadening the theoretical framework of quantum algebra structures.

Contribution

It provides a unified generalization of existing results, establishing necessary and sufficient conditions for quantum Drinfeld orbifold algebras.

Findings

Generalized conditions for quantum Drinfeld orbifold algebras

Unified framework encompassing previous algebraic structures

Extended theorems to broader classes of quantum algebras

Abstract

Quantum Drinfeld orbifold algebras are the generalizations of Drinfeld orbifold algebras, which are obtained by replacing polynomial rings by quantum polynomial rings. Shepler and Witherspoon in their paper, give necessary and sufficient conditions on a defining parameters to obtain Drinfeld orbifold algebras. In this article we generalize their result. It also simultaneously generalizes the result of Levandovskyy and Shepler about quantum Drinfeld Hecke algebras.