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Crossed products by a coalgebra

1997; Taylor & Francis; Volume: 25; Issue: 11 Linguagem: Inglês

10.1080/00927879708826070

1532-4125

Tomasz Brzeziński,

Homotopy and Cohomology in Algebraic Topology

Abstract We introduce the notion of a crossed product of an al¬gebra by a coalgebra C, which generalises the notion of a crossed product by a bialgebra well-studied in the theory of Hopf algebras. The result of such a crossed product is an algebra which is also a right C-comodule. We find the necessary and sufficient conditions for two coalgebra crossed products be equivalent. We show that the two-dimensional quantum Euclidean group is a coalgebra crossed product. The paper is completed with an appendix describing the dualisation of construction of coalgebra crossed products.