Crossed Products by a Coalgebra
Abstract
Description
We introduce the notion of a crossed product of an algebra 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.
21 pages, LaTeX, uses epsf. An error in the main proposition corrected. Will appear in Communications in Algebra
21 pages, LaTeX, uses epsf. An error in the main proposition corrected. Will appear in Communications in Algebra