BIINVERTIBLE ACTIONS OF HOPF-ALGEBRAS

We study actions of a Hopf algebra H on an algebra R such that the action is twisted by an invertible map sigma: H x H --> R; the biinvertible condition means that these actions also have both an inverse and an antiinverse in Hom(H, End R). When R is an ordinary H-module algebra, the action is biinvertible if the antipose is bijective. As a new example we show that if the H-action is twisted and the coradical of H is cocommutative, then the action is biinvertible. After studying the continuity of these actions with respect to the filter of ideals of R with zero annihilator, we consider when the actions may be extended to the symmetric Martindale quotient ring of R and its H-analog. Our results can be applied to crossed products R#(sigma) H.