Geodesic
Categorically Morita Equivalent Compact Quantum Groups
Documenta mathematica, Tome 23 (2018), pp. 2165-2216.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We give a dynamical characterization of categorical Morita equivalence between compact quantum groups. More precisely, by a Tannaka-Krein type duality, a unital $\mathrm{C}^\ast$-algebra endowed with commuting actions of two compact quantum groups corresponds to a bimodule category over their representation categories. We show that this bimodule category is invertible if and only if the actions are free, with finite dimensional fixed point algebras, which are in duality as Frobenius algebras in an appropriate sense. This extends the well-known characterization of monoidal equivalence in terms of bi-Hopf-Galois objects.
Classification : 81R15, 18D10, 46L89
Keywords: quantum group, categorical duality, Morita equivalence 
@article{DOCMA_2018__23__a0,
     author = {Neshveyev, Sergey and Yamashita, Makoto},
     title = {Categorically {Morita} {Equivalent} {Compact} {Quantum} {Groups}},
     journal = {Documenta mathematica},
     pages = {2165--2216},
     publisher = {mathdoc},
     volume = {23},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a0/}
}
TY  - JOUR
AU  - Neshveyev, Sergey
AU  - Yamashita, Makoto
TI  - Categorically Morita Equivalent Compact Quantum Groups
JO  - Documenta mathematica
PY  - 2018
SP  - 2165
EP  - 2216
VL  - 23
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a0/
LA  - en
ID  - DOCMA_2018__23__a0
ER  - 
%0 Journal Article
%A Neshveyev, Sergey
%A Yamashita, Makoto
%T Categorically Morita Equivalent Compact Quantum Groups
%J Documenta mathematica
%D 2018
%P 2165-2216
%V 23
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a0/
%G en
%F DOCMA_2018__23__a0
Neshveyev, Sergey; Yamashita, Makoto. Categorically Morita Equivalent Compact Quantum Groups. Documenta mathematica, Tome 23 (2018), pp. 2165-2216. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a0/