by Carnovale, Giovanna

We show which H

op
-cleft extensions % MathType!Translator!2!1!AMS LaTeX.tdl!TeX — AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYd
% f9irVeeu0dXdh9vqqj-hEeeu0xXdbba9frFj0-OqFfea0dXdd9vqaq
% -JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaa
% biGaciaacaqabeaadaqadqaaaOqaaGqabiaa-TgacaGGJaWaaSbaaS
% qaaiabeo8aZbqabaGccaWGibWaaWbaaSqabeaacaWGVbGaamiCaaaa
% aaa!38C5!$$
k\# _{\sigma } H^{{op}}
$$ of k for a dual quasi-triangular Hopf algebra (H, r) are H-Azumaya. The result is given in terms of bijectivity of a map % MathType!Translator!2!1!AMS LaTeX.tdl!TeX — AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYd
% f9irVeeu0dXdh9vqqj-hEeeu0xXdbba9frFj0-OqFfea0dXdd9vqaq
% -JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaa
% biGaciaacaqabeaadaqadqaaaOqaaiabeI7aXnaaBaaaleaacqaHdp
% WCaeqaaOGaaiOoaiaadIeacqGHsgIRcaWGibGaaiOkaaaa!3AEE!
$$
\theta _{\sigma } :H \to H*
$$ defined in terms of the universal r-form r and the 2-cocycle σ, generalizing a well-known result for the commutative and co-commutative case. We illustrate the Theorem with an explicit computation for the Hopf algebras of type E(n).

DOI: 10.1007/s10468-005-9000-3
Online Date: 3/16/2006
Print publication date: 2/1/2006
View article on SpringerLink