Crossed products and generalized inner actions of Hopf algebras
نویسندگان
چکیده
منابع مشابه
Full Crossed Products by Hopf C∗-algebras
We show that when a co-involutive Hopf C *-algebra S coacts via δ on a C *-algebra A, there exists a full crossed product A × δ S, with universal properties analogous to those of full crossed products by locally compact groups. The dual Hopf C *-algebra is then defined byˆS := C × id S.
متن کاملCrossed Products and Cleft Extensions for Coquasi-hopf Algebras
The notion of crossed product with a coquasi-Hopf algebra H is introduced and studied. The result of such a crossed product is an algebra in the monoidal category of right H-comodules. We give necessary and sufficient conditions for two crossed products to be equivalent. Then, two structure theorems for coquasi Hopf modules are given. First, these are relative Hopf modules over the crossed prod...
متن کاملCrossed Products by Twisted Partial Actions and Graded Algebras
For a twisted partial action Θ of a group G on an (associative nonnecessarily unital) algebra A over a commutative unital ring k, the crossed product A⋊ΘG is proved to be associative. Given a G-graded k-algebra B = ⊕g∈GBg with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B1⋊ΘG for some twisted partial action of G on ...
متن کاملActions of Hopf algebras ∗
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...
متن کاملActions 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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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1991
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1991.150.241