Twisting algebras using non-commutative torsors

TL;DR

This paper explores how non-commutative torsors can be used to twist comodule algebras, providing new presentations and examples like quantum affine spaces and tori.

Contribution

It extends existing theory on twisting algebras with non-commutative torsors and offers explicit generators and relations for the resulting algebras.

Findings

Presented a theorem for algebra presentations after twisting.

Constructed new examples of quantum affine spaces.

Developed new quantum tori constructions.

Abstract

Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can be used to twist comodule algebras. After surveying and extending the literature on the subject, we prove a theorem that affords a presentation by generators and relations for the algebras obtained by such twisting. We give a number of examples, including new constructions of the quantum affine spaces and the quantum tori.