Crossed Products by a Coalgebra
q-alg
2008-02-03 v2 Quantum Algebra
Abstract
We introduce the notion of a crossed product of an algebra by a coalgebra , 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 -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.
Keywords
Cite
@article{arxiv.q-alg/9603016,
title = {Crossed Products by a Coalgebra},
author = {Tomasz Brzezinski},
journal= {arXiv preprint arXiv:q-alg/9603016},
year = {2008}
}
Comments
21 pages, LaTeX, uses epsf. An error in the main proposition corrected. Will appear in Communications in Algebra