Idempotent states and the inner linearity property

Details Idempotent states and the inner linearity property Idempotent states and the inner linearity property

2011-12-21

arxiv.org/abs/1112.5018v2

Bull. Pol. Acad. Sci. Math. 60 (2012), 123-132

Mathematics

Quantum Algebra

9 pages

Scientific paper

We find an analytic formulation of the notion of Hopf image, in terms of the associated idempotent state. More precisely, if $\pi:A\to M_n(\mathbb C)$ 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 Ces\`aro limit of the linear functional $\phi=tr\circ\pi$. We discuss then some consequences of this result, notably to inner linearity questions.

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