Open Access
December 2009 Tracial States on the $\theta$-deformed Plane
Tokyo J. Math. 32(2): 537-547 (December 2009). DOI: 10.3836/tjm/1264170248


Starting from a trivial pure state $\Psi^{0}$, we construct non-trivial tracial states $(\Psi^{i})$ on the $\theta$-deformed $2m$-plane $C^{alg}(\mathbb{R}_{\theta}^{2m})$. Furthermore we generalize $\Psi^{i}$ to another tracial state on $C^{alg}(\mathbb{R}_{\theta}^{2m})$. We study extreme points of the tracial state space of $C^{alg}(\mathbb{R}_{\theta}^{2m})$ in the case that deformation parameters are irrational numbers. Non-trivial pure states $(\Phi_{t}^{k})$ on $C^{alg}(\mathbb{R}_{\theta}^{2m})$ are also given.


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Ken MIYAKE. "Tracial States on the $\theta$-deformed Plane." Tokyo J. Math. 32 (2) 537 - 547, December 2009.


Published: December 2009
First available in Project Euclid: 22 January 2010

zbMATH: 1196.58003
MathSciNet: MR2589961
Digital Object Identifier: 10.3836/tjm/1264170248

Rights: Copyright © 2009 Publication Committee for the Tokyo Journal of Mathematics

Vol.32 • No. 2 • December 2009
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