Quantum symmetry groups of C*-algebras equipped with orthogonal filtrations

Details Quantum symmetry groups of C*-algebras equipped with orthogonal filtrations Quantum symmetry groups of C*-algebras equipped with orthogonal filtrations

2011-09-28

arxiv.org/abs/1109.6184v1

Mathematics

Operator Algebras

31 pages

Scientific paper

Motivated by the work of Goswami on quantum isometry groups of noncommutative manifolds we define the quantum symmetry group of a unital C*-algebra A equipped with an orthogonal filtration as the universal object in the category of compact quantum groups acting on A in a filtration preserving fashion. The existence of such a universal object is proved and several examples discussed. In particular we study the universal quantum group acting on the dual of the free group and preserving both the word length and the block length.

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