Comodule algebras and 2-cocycles over the (Braided) Drinfeld double

Laugwitz, Robert

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.

Citation

Laugwitz, R. (2019). Comodule algebras and 2-cocycles over the (Braided) Drinfeld double. Communications in Contemporary Mathematics, 21(04), Article 1850045. https://doi.org/10.1142/S0219199718500451

• Journal Article Type: Article
• Acceptance Date: May 24, 2018
• Online Publication Date: Aug 30, 2019
• Publication Date: Jun 1, 2019
• Deposit Date: Dec 18, 2019
• Publicly Available Date: Dec 20, 2019
• Journal: Communications in Contemporary Mathematics
• Print ISSN: 0219-1997
• Electronic ISSN: 1793-6683
• Publisher: World Scientific
• Peer Reviewed: Peer Reviewed
• Volume: 21
• Issue: 04
• Article Number: 1850045
• DOI: https://doi.org/10.1142/S0219199718500451
• Keywords: Braided Hopf algebras; comodule algebras; 2-cocycles; Drinfeld double; quantum groups; double bosonization
• Public URL: https://nottingham-repository.worktribe.com/output/3596818
• Publisher URL: https://www.worldscientific.com/doi/abs/10.1142/S0219199718500451
• Additional Information: Electronic version of an article published as Communications in Contemporay Mathematics https://www.worldscientific.com/doi/abs/10.1142/S0219199718500451 © copyright World Scientific Publishing Company https://www.worldscientific.com/worldscinet/ccm