Crossed Products by a Coalgebra

Details Crossed Products by a Coalgebra Crossed Products by a Coalgebra

1996-03-18

arxiv.org/abs/q-alg/9603016v2

Mathematics

Quantum Algebra

21 pages, LaTeX, uses epsf. An error in the main proposition corrected. Will appear in Communications in Algebra

Scientific paper

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.

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