Hopf bimodules are modules over a diagonal crossed product algebra

Details Hopf bimodules are modules over a diagonal crossed product algebra Hopf bimodules are modules over a diagonal crossed product algebra

2001-03-08

arxiv.org/abs/math/0103057v1

Mathematics

Quantum Algebra

8 pages, Latex, no figures

Scientific paper

If H is a finite dimensional Hopf algebra, C. Cibils and M. Rosso found an algebra X having the property that Hopf bimodules over H^* coincide with left X-modules. We find two other algebras, Y and Z, having the same property; namely, Y is the "two-sided crossed product" H^*#(H\otimes H^{op})# H^{* op} and Z is the "diagonal crossed product" (H^*\otimes H^{*op})\bowtie (H\otimes H^{op}) (both concepts are due to F. Hausser and F. Nill). We also find explicit isomorphisms between the algebras X, Y, Z.

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