Yetter--Drinfeld structures on Heisenberg doubles and chains
Quantum Algebra
2009-10-15 v3 High Energy Physics - Theory
Rings and Algebras
Abstract
For a Hopf algebra B with bijective antipode, we show that the Heisenberg double H(B^*) is a braided commutative Yetter--Drinfeld module algebra over the Drinfeld double D(B). The braiding structure allows generalizing H(B^*) = B^{*cop}\braid B to "Heisenberg n-tuples" and "chains" ...\braid B^{*cop}\braid B \braid B^{*cop}\braid B\braid..., all of which are Yetter--Drinfeld D(B)-module algebras. For B a particular Taft Hopf algebra at a 2p-th root of unity, the construction is adapted to yield Yetter--Drinfeld module algebras over the 2p^3-dimensional quantum group U_qsl(2).
Keywords
Cite
@article{arxiv.0908.3105,
title = {Yetter--Drinfeld structures on Heisenberg doubles and chains},
author = {A. M. Semikhatov},
journal= {arXiv preprint arXiv:0908.3105},
year = {2009}
}
Comments
17 pages, amsart, times. V3: Multiple braided products are treated more generally and are defined so as to be YD module algebras