Quantum families of maps and quantum semigroups on finite quantum spaces

Details Quantum families of maps and quantum semigroups on finite quantum spaces Quantum families of maps and quantum semigroups on finite quantum spaces

2006-10-30

arxiv.org/abs/math/0610922v5

J. Geom. Phys. 59 (2009) 354-368

Mathematics

Operator Algebras

update: last section generalized to non-tracial states

Scientific paper

Quantum families of maps between quantum spaces are defined and studied. We
prove that quantum semigroup (and sometimes quantum group) structures arise
naturally on such objects out of more fundamental properties. As particular
cases we study quantum semigroups of maps preserving a fixed state and quantum
commutants of given quantum families of maps.

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