Lattice of Idempotent States on a Locally Compact Quantum Group
Paweł Kasprzak
University of Warsaw, PolandPiotr M. Sołtan
University of Warsaw, Poland
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Abstract
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 (-weakly continuous) idempotent states are investigated and a duality between normal idempotent states on a locally compact quantum group and on its dual is established. Additionally we analyze the question of 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.
Cite this article
Paweł Kasprzak, Piotr M. Sołtan, Lattice of Idempotent States on a Locally Compact Quantum Group. Publ. Res. Inst. Math. Sci. 56 (2020), no. 1, pp. 33–53
DOI 10.4171/PRIMS/56-1-3