Actions of Pointed Hopf Algebras
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چکیده
Definition 1.2 The invariants of H in A is the set A of those a ∈ A, that ha = ε(h)a for each h ∈ H. Straightforvard computations shows, that A is the subalgebra of A. We refer reader to [5], [6] for the basic information concerning Hopf algebras and their actions on associative algebras. As a generalization of the well-known fact for group actions the following question raised in [5] ( Question 4.2.6.) Question 1.3 If A is a commutative k-algebra and H any finite dimensional Hopf algebra such that A is H-module algebra, is A integral over A ? If A is an affine algebra, then Artin-Tate lemma ensures that A is also affine. Some positive answers to question 1.3 are known.
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