On actions of connected Hopf algebras
نویسندگان
چکیده
Let H H be a connected Hopf algebra acting on an A"> A encoding="application/x-tex">A . Working over base field having characteristic alttext="0"> 0 encoding="application/x-tex">0 , we show that for given prime (semi-prime, completely prime) ideal I"> I encoding="application/x-tex">I of the largest -stable A contained in is also prime). We prove similar result certain subrings convolution algebras.
منابع مشابه
Actions of Hopf algebras on noncommutative algebras
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 ...
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An action of a finite dimensional Hopf algebra H on a noncommutative associative algebra A is considered. Properties of A , the subalgebra of invariants in A, are studied. It is proved that if A is integral over Z(A), the centre of an algebra A, then A is integral over Z(A) H , the subalgebra of invariants in Z(A), for each of three cases: 1. the coradical H0 is cocommutative and char k = p > 0...
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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] ( Questio...
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William M. Singer’s theory of extensions of connected Hopf algebras is used to give a complete list of the cocommutative connected Hopf algebras over a field of positive characteristic p which have vector space dimension less than or equal to p3. The theory shows that there are exactly two noncommutative non-primitively generated Hopf algebras on the list, one of which is the Hopf algebra corre...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2021
ISSN: ['2330-1511']
DOI: https://doi.org/10.1090/proc/15377