Geodesic
Actions, Quotients and Lattices of Locally Compact Quantum Groups
Documenta mathematica, Tome 25 (2020), pp. 2553-2582
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

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).
DOI : 10.4171/dm/807
Classification : 20G42, 46L30, 46L65
Mots-clés : lattice, locally compact quantum group, property (T), weight, canonical implementation, closed quantum subgroup 
@article{10_4171_dm_807,
     author = {Ami Viselter and Alexandru Chirvasitu and Michael Brannan},
     title = {Actions, {Quotients} and {Lattices} of {Locally} {Compact} {Quantum} {Groups}},
     journal = {Documenta mathematica},
     pages = {2553--2582},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/807},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/807/}
}
TY  - JOUR
AU  - Ami Viselter
AU  - Alexandru Chirvasitu
AU  - Michael Brannan
TI  - Actions, Quotients and Lattices of Locally Compact Quantum Groups
JO  - Documenta mathematica
PY  - 2020
SP  - 2553
EP  - 2582
VL  - 25
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/807/
DO  - 10.4171/dm/807
ID  - 10_4171_dm_807
ER  - 
%0 Journal Article
%A Ami Viselter
%A Alexandru Chirvasitu
%A Michael Brannan
%T Actions, Quotients and Lattices of Locally Compact Quantum Groups
%J Documenta mathematica
%D 2020
%P 2553-2582
%V 25
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/807/
%R 10.4171/dm/807
%F 10_4171_dm_807
Ami Viselter; Alexandru Chirvasitu; Michael Brannan. Actions, Quotients and Lattices of Locally Compact Quantum Groups. Documenta mathematica, Tome 25 (2020), pp. 2553-2582. doi: 10.4171/dm/807

Cité par Sources :