Idempotent states on locally compact quantum groups

Details Idempotent states on locally compact quantum groups Idempotent states on locally compact quantum groups

2011-02-10

arxiv.org/abs/1102.2051v2

Mathematics

Operator Algebras

23 pages, v2 adds a discussion of the coamenability of some examples of locally compact quantum groups and corrects a few mino

Scientific paper

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.

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