Quantum automorphism groups of connected locally finite graphs
Lukas Rollier (KU Leuven)
Thursday 12th January 16:00-17:00 Maths 311B
A very natural construction by Banica yields for any finite graph its quantum automorphism group. Recently, through work of Mančinska and Roberson, the representation category of these quantum groups has been described combinatorially. Building on these combinatorial tools, it is possible to build a unitary tensor category for every connected locally finite graph, and through a Tannaka-Krein type reconstruction, these may be used to define quantum automorphism groups of connected locally finite graphs as algebraic locally compact quantum groups. In this talk, I will give a broad overview of this construction, and if time permits, describe how it may be applied to define ‘quantizations’ of finitely generated groups.
This has been joint work with Stefaan Vaes.