Truncation and Duality Results for Hopf Image Algebras

Teodor Banica. "Truncation and Duality Results for Hopf Image Algebras." Bulletin of the Polish Academy of Sciences. Mathematics 62.2 (2014): 161-179. <http://eudml.org/doc/281262>.

@article{TeodorBanica2014,
abstract = {Associated to an Hadamard matrix $H ∈ M_N(ℂ)$ is the spectral measure μ ∈ [0,N] of the corresponding Hopf image algebra, A = C(G) with $G ⊂ S⁺_N$. We study a certain family of discrete measures $μ^r ∈ [0,N]$, coming from the idempotent state theory of G, which converge in Cesàro limit to μ. Our main result is a duality formula of type $∫_0^N (x/N)^p dμ^r(x) = ∫_0^N (x/N)^r dν^p(x)$, where $μ^r,ν^r$ are the truncations of the spectral measures μ,ν associated to $H,H^t$. We also prove, using these truncations $μ^r,ν^r$, that for any deformed Fourier matrix $H=F_M ⊗_Q F_N$ we have μ = ν.},
author = {Teodor Banica},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {quantum permutation; Hadamard matrix},
language = {eng},
number = {2},
pages = {161-179},
title = {Truncation and Duality Results for Hopf Image Algebras},
url = {http://eudml.org/doc/281262},
volume = {62},
year = {2014},
}

TY - JOUR
AU - Teodor Banica
TI - Truncation and Duality Results for Hopf Image Algebras
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2014
VL - 62
IS - 2
SP - 161
EP - 179
AB - Associated to an Hadamard matrix $H ∈ M_N(ℂ)$ is the spectral measure μ ∈ [0,N] of the corresponding Hopf image algebra, A = C(G) with $G ⊂ S⁺_N$. We study a certain family of discrete measures $μ^r ∈ [0,N]$, coming from the idempotent state theory of G, which converge in Cesàro limit to μ. Our main result is a duality formula of type $∫_0^N (x/N)^p dμ^r(x) = ∫_0^N (x/N)^r dν^p(x)$, where $μ^r,ν^r$ are the truncations of the spectral measures μ,ν associated to $H,H^t$. We also prove, using these truncations $μ^r,ν^r$, that for any deformed Fourier matrix $H=F_M ⊗_Q F_N$ we have μ = ν.
LA - eng
KW - quantum permutation; Hadamard matrix
UR - http://eudml.org/doc/281262
ER -