Comodule Algebras and 2-Cocycles over the (Braided) Drinfeld Double
Abstract
We show that for dually paired bialgebras, every comodule algebra over one of the paired bialgebras gives a comodule algebra over their Drinfeld double via a crossed product construction. These constructions generalize to working with bialgebra objects in a braided monoidal category of modules over a quasitriangular Hopf algebra. Hence two ways to provide comodule algebras over the braided Drinfeld double (the double bosonization) are provided. Furthermore, a map of second Hopf algebra cohomology spaces is constructed. It takes a pair of 2-cocycles over dually paired Hopf algebras and produces a 2-cocycle over their Drinfeld double. This construction also has an analogue for braided Drinfeld doubles.
Keywords
Cite
@article{arxiv.1708.02641,
title = {Comodule Algebras and 2-Cocycles over the (Braided) Drinfeld Double},
author = {Robert Laugwitz},
journal= {arXiv preprint arXiv:1708.02641},
year = {2020}
}
Comments
34 pages, several figures created with Inkscape. Version 2: more references added, small typos corrected. Version 3: Small corrections and further references added. To appear in Comm. Contemp. Math