2022/02/25 by Alexandru Chirvăsitu, Chirvasitu, Alexandru
Mathematics · #20G42 #22D10 #22D25 #46L67 #47L65 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2202.12766
openalex publication_date 2022/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that for a closed embedding ℍ≤ \mathbbG of locally compact quantum groups (LCQGs) with \mathbbG/ℍ admitting an invariant probability measure, a unitary \mathbbG-representation is type-I if its restriction to ℍ is. On a related note, we also prove that if an action \mathbbG\circlearrowright A of an LCQG on a unital C^*-algebra admits an invariant state then the full group algebra of \mathbbG embeds into the resulting full crossed product (and into the multiplier algebra of that crossed product if the original algebra is not unital). We also prove a few other results on crossed products of LCQG actions, some of which seem to be folklore; among them are (a) the fact that two mutually dual quantum-group morphisms produce isomorphic full crossed products, and (b) the fact that full and reduced crossed products by dual-coamenable LCQGs are isomorphic.