Complete positivity of Rieffel’s deformation quantization by actions of

  • Daniel Kaschek

    University of Freiburg, Germany
  • Nikolai Neumaier

    University of Freiburg, Germany
  • Stefan Waldmann

    University of Freiburg, Germany

Abstract

In this paper we consider -algebraic deformations by actions of 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 . J. Noncommut. Geom. 3 (2009), no. 3, pp. 361–375

DOI 10.4171/JNCG/40