Article (Scientific journals)
Representations of quantum permutation algebras
Schlenker, Jean-Marc; Banica, Teodor; Bichon, Julien
2009In Journal of Functional Analysis, 257 (9), p. 2864-2910
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Keywords :
Quantum permutation; Hadamard matrix
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
Schlenker, Jean-Marc ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Banica, Teodor
Bichon, Julien
External co-authors :
yes
Language :
English
Title :
Representations of quantum permutation algebras
Publication date :
2009
Journal title :
Journal of Functional Analysis
ISSN :
1096-0783
Publisher :
Academic Press
Volume :
257
Issue :
9
Pages :
2864-2910
Peer reviewed :
Peer Reviewed verified by ORBi
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since 11 February 2016

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