### Abstract

Looking for the universal covering of the smooth noncommutative torus leads to a curve of associative multiplications on the space O′_{M} (ℝ^{2n}) ≅ O_{C}(ℝ^{2n}) of L. Schwartz which is smooth in the deformation parameter (latin small letter h with stroke). The Taylor expansion in (latin small letter h with stroke) leads to the formal Moyal star product. The noncommutative torus and this version of the Heisenberg plane are examples of smooth *-algebras: smooth in the sense of having many derivations. A tentative definition of this concept is given.

Original language | English |
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Pages (from-to) | 54-78 |

Number of pages | 25 |

Journal | Progress of Theoretical Physics Supplement |

Issue number | 144 |

Publication status | Published - 2001 Dec 1 |

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

Dubois-Violette, M., Kriegl, A., Maeda, Y., & Michor, P. W. (2001). Smooth *-algebras.

*Progress of Theoretical Physics Supplement*, (144), 54-78.