Twisting algebras using non-commutative torsors
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.
Cite
@article{arxiv.0911.5287,
title = {Twisting algebras using non-commutative torsors},
author = {Pierre Guillot and Christian Kassel and Akira Masuoka},
journal= {arXiv preprint arXiv:0911.5287},
year = {2013}
}
Comments
27 pages. Masuoka is a new coauthor. Introduction was revised. Sections 1 and 2 were thoroughly restructured. The presentation theorem in Section 3 is now put in a more general framework and has a more general formulation. Section 4 was shortened. All examples (quantum affine spaces and tori, twisting of SL(2), twisting of the enveloping algebra of sl(2)) are left unchanged