Models of quantum permutations

2019/06/25 by Jung, Stefan, Weber, Moritz · 1 citation
#FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1906.10409

Abstract

For N≥ 4 we present a series of *-homomorphisms φ_n:C(S_N⁺)→ B_n where S_N⁺ is the quantum permutation group. They are not necessarily representations of the quantum group S_N⁺ but they yield good operator algebraic models of quantum permutation matrices. The C*-algebras B_n allow the construction of an inverse limit B_∞ which defines a compact matrix quantum group S_N\subsetneq G⊆ S_N⁺. We know G=S_N⁺ for N=4,5 from Banica's work, but we have to leave open the case N≥ 6.

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• Hypercube C*-algebras and an application to magic isometries

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