States of Toeplitz-Cuntz algebras
Abstract
We characterize the state space of a Toeplitz-Cuntz algebra TOn in terms of positive operator matrices on Fock space which satisfy sl() , where sl() is the operator matrix obtained from by taking the trace in the last variable. Essential states correspond to those matrices which are slice-invariant. As an application we show that a pure essential product state of the fixed-point algebra for the action of the gauge group has precisely a circle of pure extensions to TOn.
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