Idempotent States and the Inner Linearity Property

• Autorzy: Banica, T. , Franz, U. , Skalski, A.
• Języki publikacji: EN

Abstrakty

EN

We find an analytic formulation of the notion of Hopf image, in terms of the associated idempotent state. More precisely, if π:A→M_n(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.

Słowa kluczowe

EN

idempotent state; Hopf image; inner linearity

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: Vol. 60, no 2
• Strony: 123--132
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Banica, T.

• Department of Mathematics Cergy-Pontoise University 95000 Cergy-Pontoise, France,

autor

Franz, U.

• Department of Mathematics University of Franche-Comté 16 route de Gray 25030 Besançon Cedex, France,

autor

Skalski, A.

• Institute of Mathematics Polish Academy of Sciences Sniadeckich 8 P.O. Box 21 00-956 Warszawa, Poland,

Bibliografia

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Identyfikatory

DOI

10.4064/ba60-2-3