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Truncation and Duality Results for Hopf Image Algebras

Banica T.

Bulletin of the Polish Academy of Sciences. Mathematics

2014

Vol. 62, no 2

161--179

Associated to an Hadamard matrix H∈MN(C) is the spectral measure μ∈P[0,N] of the corresponding Hopf image algebra, A=C(G) with G⊂S+N. We study a certain family of discrete measures μr∈P[0,N], coming from the idempotent state theory of G, which converge in Cesàro limit to μ. Our main result is a duality formula of type ∫N0(x/N)pdμr(x)=∫N0(x/N)rdνp(x), where μr,νr are the truncations of the spectral measures μ,ν associated to H,Ht. We also prove, using these truncations μr,νr, that for any deformed Fourier matrix H=FM⊗QFN we have μ=ν.