2018/02/12 by Kasprzak, Paweł, Sołtan, Piotr M.
#20G42 #43A05 #46L89 #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1802.03953
We study lattice operations on the set of idempotent states on a locally compact quantum group corresponding to the operations of intersection of compact subgroups and forming the subgroup generated by two compact subgroups. Normal (σ-weakly continuous) idempotent states are investigated and a duality between normal idempotent states on a locally compact quantum group \mathbbG and on its dual \widehat\mathbbG is established. Additionally we analyze the question when a left coideal corresponding canonically to an idempotent state is finite dimensional and give a characterization of normal idempotent states on compact quantum groups.