Hopf Galois Extension in Braided Tensor Categories

Abstract

The relation between crossed product and $H$-Galois extension in braided tensor category $\mathcal{C}$ 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 $\mathcal{C}$, then $A = B #_σH$ 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 $\mathcal{C}$.

26 pages

References in corpus (1)

• Duality Theorem and Drinfeld Double in Braided Tensor Categories