Smooth *-algebras

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

    Research output: Contribution to journalArticle

    11 Citations (Scopus)

    Abstract

    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 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.