TY - JOUR

T1 - Central Invariants of H-module algebras

AU - Cohen, Miriam

AU - Westreich, Sara

PY - 1993/1/1

Y1 - 1993/1/1

N2 - Let H be a Hopf algebra over a field k, and A an H-module algebra, with subalgebra of H-invariants denoted by AH. When (H, R) is quasitriangular and A is quantum commutative with respect to (H, R), (e.g. quantum planes, graded commutative superalgebras), then [formula ommitted] center of A =Z(A). In this paper we are mainly concerned with actions of H for which AH⊂ Z(A). We show that under this hypothesis there exists strong relations between the ideal structures of AH, A and A#H. We demonstrate the theorems by constructing an example of a quantum commutative A, so that A/AHis H*-Galois. This is done by giving (C G)*, G = Zn X Zn,a nontrivial quasitriangular structure and defining an action of it on a localization of the quantum plane.

AB - Let H be a Hopf algebra over a field k, and A an H-module algebra, with subalgebra of H-invariants denoted by AH. When (H, R) is quasitriangular and A is quantum commutative with respect to (H, R), (e.g. quantum planes, graded commutative superalgebras), then [formula ommitted] center of A =Z(A). In this paper we are mainly concerned with actions of H for which AH⊂ Z(A). We show that under this hypothesis there exists strong relations between the ideal structures of AH, A and A#H. We demonstrate the theorems by constructing an example of a quantum commutative A, so that A/AHis H*-Galois. This is done by giving (C G)*, G = Zn X Zn,a nontrivial quasitriangular structure and defining an action of it on a localization of the quantum plane.

UR - http://www.scopus.com/inward/record.url?scp=21144471749&partnerID=8YFLogxK

U2 - 10.1080/00927879308824709

DO - 10.1080/00927879308824709

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AN - SCOPUS:21144471749

SN - 0092-7872

VL - 21

SP - 2859

EP - 2883

JO - Communications in Algebra

JF - Communications in Algebra

IS - 8

ER -