JournalsjncgVol. 3, No. 3pp. 361–375

Complete positivity of Rieffel’s deformation quantization by actions of ℝ<sup><var>d</var></sup>

  • Daniel Kaschek

    University of Freiburg, Germany
  • Nikolai Neumaier

    University of Freiburg, Germany
  • Stefan Waldmann

    University of Freiburg, Germany
Complete positivity of Rieffel’s deformation quantization by actions of ℝ<sup><var>d</var></sup> cover
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Abstract

In this paper we consider C*-algebraic deformations by actions of ℝd à la Rieffel and show that every state of the undeformed algebra can be deformed into a state of the deformed algebra in the sense of a continuous field of states. The construction is explicit and involves a convolution operator with a particular Gauß function.

Cite this article

Daniel Kaschek, Nikolai Neumaier, Stefan Waldmann, Complete positivity of Rieffel’s deformation quantization by actions of ℝ<sup><var>d</var></sup>. J. Noncommut. Geom. 3 (2009), no. 3, pp. 361–375

DOI 10.4171/JNCG/40