Geodesic
Actions, Quotients and Lattices of Locally Compact Quantum Groups
Documenta mathematica, Tome 25 (2020), pp. 2553-2582.

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

We prove a number of property (T) permanence results for locally compact quantum groups under exact sequences and the presence of invariant states, analogous to their classical versions. Along the way we characterize the existence of invariant weights on quantum homogeneous spaces of quotient type, and relate invariant states for LCQG actions on von Neumann algebras to invariant vectors in canonical unitary implementations, providing an application to amenability. Finally, we introduce a notion of lattice in a locally compact quantum group, noting examples provided by Drinfeld doubles of compact quantum groups. We show that property (T) lifts from a lattice to the ambient LCQG, just as it does classically, thus obtaining new examples of non-classical, non-compact, non-discrete LCQGs with property (T).
Classification : 20G42, 46L65, 46L30
Keywords: locally compact quantum group, property (T), lattice, weight, canonical implementation, closed quantum subgroup 
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     author = {Brannan, Michael and Chirvasitu, Alexandru and Viselter, Ami},
     title = {Actions, {Quotients} and {Lattices} of {Locally} {Compact} {Quantum} {Groups}},
     journal = {Documenta mathematica},
     pages = {2553--2582},
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     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a0/}
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Brannan, Michael; Chirvasitu, Alexandru; Viselter, Ami. Actions, Quotients and Lattices of Locally Compact Quantum Groups. Documenta mathematica, Tome 25 (2020), pp. 2553-2582. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a0/