Smooth *-algebras

Michel Dubois-Violette, Andreas Kriegl, Yoshiaki Maeda, Peter W. Michor

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Looking for the universal covering of the smooth noncommutative torus leads to a curve of associative multiplications on the space O′M (ℝ2n) ≅ OC(ℝ2n) 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 languageEnglish
Pages (from-to)54-78
Number of pages25
JournalProgress of Theoretical Physics Supplement
Issue number144
Publication statusPublished - 2001
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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