Yetter-Drinfeld modules under cocycle twists

[摘要] We give an explicit formula for the correspondence between simple Yetter-Drinfeld modules for certain finite-dimensional pointed Hopf algebras H and those for cocycle twists H-sigma of H. This implies an equivalence between modules for their Drinfeld doubles. To illustrate our results, we consider the restricted two-parameter quantum groups u(r,s)(sl(n)) under conditions on the parameters guaranteeing that u(r,s)(sl(n)) is a Drinfeld double of its Borel subalgebra. We determine explicit correspondences between u(r,s)(sl(n))-modules for different values of r and s and provide examples where no such correspondence can exist. Our examples were obtained via the computer algebra system SINGULAR::PLURAL. (C) 2009 Elsevier Inc. All rights reserved.

[发布日期] 2010-12-01

[关键词] Hopf algebra;Cocycle twist;Yetter-Drinfeld module;Drinfeld double;Two-parameter quantum group