Reference : Representations of quantum permutation algebras
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/24535
Representations of quantum permutation algebras
English
Schlenker, Jean-Marc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Banica, Teodor []
Bichon, Julien []
2009
Journal of Functional Analysis
Academic Press
257
9
2864-2910
Yes (verified by ORBilu)
International
0022-1236
1096-0783
[en] Quantum permutation ; Hadamard matrix
[en] We develop a combinatorial approach to the quantum permutation algebras, as Hopf images of representations of type π:As(n)→B(H)π:As(n)→B(H). We discuss several general problems, including the commutativity and cocommutativity ones, the existence of tensor product or free wreath product decompositions, and the Tannakian aspects of the construction. The main motivation comes from the quantum invariants of the complex Hadamard matrices: we show here that, under suitable regularity assumptions, the computations can be performed up to n=6.
http://hdl.handle.net/10993/24535
10.1016/j.jfa.2009.04.013
http://http://arxiv.org/abs/0901.2331

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