Quantization of locally compact groups associated with essentially bijective 1-cocycles
(2024) International Journal of Mathematics — Vol. 35, n° 08, p. 23 (2024)
Files
2.pdf
Open Access - Adobe PDF
- 298.14 KB
Details
- Authors
Gayral, Victor 
Neshveyev, Sergey Tuset, Lars
- Abstract
- Given an extension of locally compact groups, with abelian, and a compatible essentially bijective -cocycle , we define a dual unitary -cocycle on and show that the associated deformation of is a cocycle bicrossed product defined by a matched pair of subgroups of . We also discuss an interpretation of our construction from the point of view of Kac cohomology for matched pairs. Our setup generalizes that of Etingof and Gelaki for finite groups and its extension due to Ben David and Ginosar, as well as our earlier work on locally compact groups satisfying the dual orbit condition. In particular, we get a locally compact quantum group from every involutive nondegenerate set-theoretical solution of the Yang–Baxter equation, or more generally, from every brace structure. On the technical side, the key new points are constructions of an irreducible projective representation of on …
- Affiliations
Citations
Bieliavsky, P., Gayral, V., Neshveyev, S., & Tuset, L. (2024). Quantization of locally compact groups associated with essentially bijective 1-cocycles. International Journal of Mathematics, 35(08), 23. https://doi.org/10.1142/s0129167x24500277 (Original work published 2024)