Hopf Galois Extension in Braided Tensor Categories

Details Hopf Galois Extension in Braided Tensor Categories Hopf Galois Extension in Braided Tensor Categories

2003-09-27

arxiv.org/abs/math/0309448v7

Mathematics

Rings and Algebras

26 pages

Scientific paper

The relation between crossed product and $H$-Galois extension in braided tensor category ${\cal C}$ with equivalisers and coequivalisers is established. That is, it is shown that if there exist an equivaliser and a coequivaliser for any two morphisms in ${\cal C}$, then $A = B #_\sigma H$ is a crossed product algebra if and only if the extension $A/B$ is Galois, the canonical epic $q: A\otimes A \to A\otimes_B A$ is split and $A$ is isomorphic as left $B$-modules and right $H$-comodules to $B\otimes H$ in ${\cal C}$.

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