Wyniki wyszukiwania - BazTech

Ograniczanie wyników

3 Bulletin of the Polish Academy of Sciences. Mathematics

Powiadomienia systemowe

Sesja wygasła!

Znaleziono wyników: 3

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Super-easy quantum groups : definition and examples

Banica T.

Bulletin of the Polish Academy of Sciences. Mathematics

2018

Vol. 66, no. 1

57--68

We investigate the “two-parameter” quantum symmetry groups that we previously constructed with Skalski, with the conclusion that some of these quantum groups, namely those without singletons, are “super-easy” in a suitable sense, which we axiomatize here. Our formalism also covers the symplectic group Spn and its free version Sp+n, and some other interesting examples. Finally, we address the general problem of classifying the super-easy quantum groups, and we make a few comments on it.

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.

Idempotent States and the Inner Linearity Property

Banica T., Franz U., Skalski A.

Bulletin of the Polish Academy of Sciences. Mathematics

2012

Vol. 60, no 2

123--132

We find an analytic formulation of the notion of Hopf image, in terms of the associated idempotent state. More precisely, if π:A→Mn(C) is a finite-dimensional representation of a Hopf C*-algebra, we prove that the idempotent state associated to its Hopf image A′ must be the convolution Cesàro limit of the linear functional φ=tr∘π. We then discuss some consequences of this result, notably to inner linearity questions.