2013/01/21 by Sergey Neshveyev, Neshveyev, Sergey, Lars Tuset +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1301.4897
openalex publication_date 2013/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a C*-algebra A with a left action of a locally compact quantum group G on it and a unitary 2-cocycle Omega on G, we define a deformation AOmega of A. The construction behaves well under certain additional technical assumptions on Omega, the most important of which is regularity, meaning that C0(G)Omega\rtimes G is isomorphic to the algebra of compact operators on some Hilbert space. In particular, then AΩis stably isomorphic to the iterated twisted crossed product Gop\ltimesΩG\ltimes A. Also, in good situations, the C*-algebra AΩcarries a left action of the deformed quantum group GΩand we have an isomorphism GΩ\ltimes AΩ≅ G\ltimes A. When G is a genuine locally compact group, we show that the action of G on C0(G)Omega=C*r( G;Omega) is always integrable. Stronger assumptions of properness and saturation of the action imply regularity. As an example, we make a preliminary analysis of the cocycles on the duals of some solvable Lie groups recently constructed by Bieliavsky et al., and discuss the relation of our construction to that of Bieliavsky and Gayral.