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Original Articles

Crossed products by a coalgebra

Pages 3551-3575 | Received 01 Jun 1996, Published online: 27 Jun 2007
 

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.

Research supported by the EPSRC grant GR/K02244

Research supported by the EPSRC grant GR/K02244

Notes

Research supported by the EPSRC grant GR/K02244

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