A rigidity conjecture by Goswami states that existence of a smooth and faithful action of a compact quantum group G on a compact connected Riemannian manifold M forces G to be compact group. In particular, whenever the action is isometric, or G is finite dimensional, Goswami and Joardar have proved that the conjecture is true. The first step in the investigation of a non-compact version of this rigidity conjecture demands a correct notion of faithful actions of locally compact quantum groups on classical spaces. In this talk, we show that bicrossed product construction for locally compact groups provides a large class of examples of non-Kac locally compact quantum groups acting faithfully and ergodically on classical (non-compact) spaces. However, none of these actions can be isometric, leading to the aforementioned rigidity conjecture may hold in the non-compact case as well. This is based on the joint work in progress with Debashish Goswami.
Venue
M3
Speaker
Sutanu Roy
Affiliation
Carleton University, Canada
Title
Faithful actions of locally compact quantum groups on classical spaces
A rigidity conjecture by Goswami states that existence of a smooth and faithful action of a compact quantum group G on a compact connected Riemannian manifold M forces G to be compact group. In particular, whenever the action is isometric, or G is finite dimensional, Goswami and Joardar have proved that the conjecture is true. The first step in the investigation of a non-compact version of this rigidity conjecture demands a correct notion of faithful actions of locally compact quantum groups on classical spaces. In this talk, we show that bicrossed product construction for locally compact groups provides a large class of examples of non-Kac locally compact quantum groups acting faithfully and ergodically on classical (non-compact) spaces. However, none of these actions can be isometric, leading to the aforementioned rigidity conjecture may hold in the non-compact case as well. This is based on the joint work in progress with Debashish Goswami. - See more at: http://sms.niser.ac.in/news/seminar-57#sthash.QhHWSEq6.dpuf
A rigidity conjecture by Goswami states that existence of a smooth and faithful action of a compact quantum group G on a compact connected Riemannian manifold M forces G to be compact group. In particular, whenever the action is isometric, or G is finite dimensional, Goswami and Joardar have proved that the conjecture is true. The first step in the investigation of a non-compact version of this rigidity conjecture demands a correct notion of faithful actions of locally compact quantum groups on classical spaces. In this talk, we show that bicrossed product construction for locally compact groups provides a large class of examples of non-Kac locally compact quantum groups acting faithfully and ergodically on classical (non-compact) spaces. However, none of these actions can be isometric, leading to the aforementioned rigidity conjecture may hold in the non-compact case as well. This is based on the joint work in progress with Debashish Goswami. - See more at: http://sms.niser.ac.in/news/seminar-57#sthash.QhHWSEq6.dpuf
A rigidity conjecture by Goswami states that existence of a smooth and faithful action of a compact quantum group G on a compact connected Riemannian manifold M forces G to be compact group. In particular, whenever the action is isometric, or G is finite dimensional, Goswami and Joardar have proved that the conjecture is true. The first step in the investigation of a non-compact version of this rigidity conjecture demands a correct notion of faithful actions of locally compact quantum groups on classical spaces. In this talk, we show that bicrossed product construction for locally compact groups provides a large class of examples of non-Kac locally compact quantum groups acting faithfully and ergodically on classical (non-compact) spaces. However, none of these actions can be isometric, leading to the aforementioned rigidity conjecture may hold in the non-compact case as well. This is based on the joint work in progress with Debashish Goswami. - See more at: http://sms.niser.ac.in/news/seminar-57#sthash.QhHWSEq6.dpuf