2011/02/10 by Pekka Salmi, Salmi, Pekka, Adam Skalski +1
Mathematics · #46L30 #60B15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L65 #Quantum Algebra (math.QA) #Secondary 43A05
paper · pdf · doi:10.48550/arxiv.1102.2051
openalex publication_date 2011/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Idempotent states on a unimodular coamenable locally compact quantum group A are shown to be in one-to-one correspondence with right invariant expected C*-subalgebras of A. Haar idempotents, that is, idempotent states arising as Haar states on compact quantum subgroups of A, are characterised and shown to be invariant under the natural action of the modular element. This leads to the one-to-one correspondence between Haar idempotents on A and right invariant symmetric expected C*-subalgebras of A without the unimodularity assumption. Finally the tools developed in the first part of the paper are applied to show that the coproduct of a coamenable locally compact quantum group restricts to a continuous coaction on each right invariant expected C*-subalgebra.