Actions of Hopf algebras on noncommutative algebras
نویسنده
چکیده
Often A is called H-module algebra. We refer reader to [11, 6] for the basic information concerning Hopf algebras and their actions on associative algebras. Definition 1.2 The invariants of H in A is the set AH of those a ∈ A, that ha = ε(h)a for each h ∈ H. Straightforward computations show, that AH is subalgebra of A. The notion of action of Hopf algebra on associative algebra generalize the notion of automorphism and derivation of associative algebra. As a generalization of the well-known fact for group actions the following question was raised in [6] (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 AH ? Some positive answers to question 1.3 are known. Theorem 1.4 ([5]) Let H be a cocommutative Hopf algebra and A be a commutative Hmodule algebra. Then A is integral extension of AH .
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