From projective representations to pentagonal cohomology via quantization

2023/05/05 by Gayral, Victor, Marie, Valentin
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2305.03389

Abstract

Given a locally compact group G=Q\ltimes V such that V is Abelian and such that the action of Q on the Pontryagin dual V has a free orbit of full measure, we construct a family of unitary dual 2-cocycles Ω_ω (aka non-formal Drinfel'd twists) whose equivalence classes [Ω_ω]∈ H²( G,\mathbb T) are parametrized by cohomology classes [ω]∈ H²(Q,\mathbb T). We prove that the associated locally compact quantum groups are isomorphic to cocycle bicrossed product quantum groups associated to a pair of subgroups of the dual semidirect product Q\ltimes V, both isomorphic to Q, and to a pentagonal cocycle Θ_ω explicitly given in terms of the group cocycle ω.

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