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- W2950673973 abstract "Let $(H,R)$ be a quasitriangular weak Hopf algebra over a field $k$. We show that there is a braided monoidal equivalence between the Yetter-Drinfeld module category $^H_Hmathscr{YD}$ over $H$ and the category of comodules over some braided Hopf algebra ${}_RH$ in the category $_Hmathscr{M}$. Based on this equivalence, we prove that every braided bi-Galois object $A$ over the braided Hopf algebra ${}_RH$ defines a braided autoequivalence of the category $^H_Hmathscr{YD}$ if and only if $A$ is quantum commutative. In case $H$ is semisimple over an algebraically closed field, i.e. the fusion case, then every braided autoequivalence of $^H_Hmathscr{YD}$ trivializable on $_Hmathscr{M}$ is determined by such a quantum commutative Galois object. The quantum commutative Galois objects in $_Hmathscr{M}$ form a group measuring the Brauer group of $(H,R)$ as studied in [20] in the Hopf algebra case." @default.
- W2950673973 created "2019-06-27" @default.
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- W2950673973 date "2013-12-13" @default.
- W2950673973 modified "2023-10-03" @default.
- W2950673973 title "Braided autoequivalences and quantum commutative bi-Galois objects" @default.
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- W2950673973 doi "https://doi.org/10.48550/arxiv.1312.3800" @default.
- W2950673973 hasPublicationYear "2013" @default.
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