Crossed products and cleft extensions for coquasi-Hopf algebras Export

@article{citeulike:4857767, abstract = {The notion of crossed product by a coquasi-bialgebra H is introduced and studied. The resulting crossed product is an algebra in the monoidal category of right H-comodules. We give an interpretation of the crossed product as an action of a monoidal category. In particular, necessary and sufficient conditions for two crossed products to be equivalent are provided. Then, two structure theorems for coquasi Hopf modules are given. First, these are relative Hopf modules over the crossed product. Second, the category of coquasi-Hopf modules is trivial, namely equivalent to the category of modules over the starting associative algebra. In connection the crossed product, we recall the notion of a cleft extension over a coquasi-Hopf algebra. A Morita context of Hom spaces is constructed in order to explain these extensions, which are shown to be equivalent with crossed product with invertible cocycle. At the end, we give a complete description of all cleft extensions by the non-trivial coquasi-Hopf algebras of dimension two and three.}, archivePrefix = {arXiv}, author = {Balan, Adriana}, citeulike-article-id = {4857767}, citeulike-linkout-0 = {http://arxiv.org/abs/0805.4204}, citeulike-linkout-1 = {http://arxiv.org/pdf/0805.4204}, day = {27}, eprint = {0805.4204}, keywords = {hopf\_algebras, quantum\_operator\_algebras}, month = {Nov}, posted-at = {2009-06-15 10:36:35}, priority = {2}, title = {Crossed products and cleft extensions for coquasi-Hopf algebras}, url = {http://arxiv.org/abs/0805.4204}, year = {2008} }

TY - JOUR ID - citeulike:4857767 L3 - citeulike-article-id:4857767 N2 - The notion of crossed product by a coquasi-bialgebra H is introduced and studied. The resulting crossed product is an algebra in the monoidal category of right H-comodules. We give an interpretation of the crossed product as an action of a monoidal category. In particular, necessary and sufficient conditions for two crossed products to be equivalent are provided. Then, two structure theorems for coquasi Hopf modules are given. First, these are relative Hopf modules over the crossed product. Second, the category of coquasi-Hopf modules is trivial, namely equivalent to the category of modules over the starting associative algebra. In connection the crossed product, we recall the notion of a cleft extension over a coquasi-Hopf algebra. A Morita context of Hom spaces is constructed in order to explain these extensions, which are shown to be equivalent with crossed product with invertible cocycle. At the end, we give a complete description of all cleft extensions by the non-trivial coquasi-Hopf algebras of dimension two and three. TI - Crossed products and cleft extensions for coquasi-Hopf algebras KW - hopf_algebras KW - quantum_operator_algebras AU - Balan, Adriana PY - 2008/Nov/27/ UR - http://arxiv.org/abs/0805.4204 ER -