Examples of quantum commutants

Details Examples of quantum commutants Examples of quantum commutants

2008-06-03

arxiv.org/abs/0806.0503v2

Arab J. Sci. Eng. 33 no. 2C (2008), 447-457

Mathematics

Quantum Algebra

11 pages, an error in one example corrected, typos corrected

Scientific paper

We describe the notion of a quantum family of maps of a quantum space and that of a quantum commutant of such a family. Quantum commutants are quantum semigroups defined by a certain universal property. We give a few examples of these objects acting on a classical $n$-point space and on the quantum space underlying the algebra of two by two matrices. We show that some of the resulting quantum semigroups are not compact quantum groups. The proof of one result touches on an interesting problem of the theory of compact quantum groups.

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