Smooth *-algebras

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

doi:10.1143/ptps.144.54

Smooth *-algebras

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

Research output: Contribution to journal › Article › peer-review

14 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) ≅ O_C(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 language	English
Pages (from-to)	54-78
Number of pages	25
Journal	Progress of Theoretical Physics Supplement
Issue number	144
DOIs	https://doi.org/10.1143/ptps.144.54
Publication status	Published - 2001
Externally published	Yes

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

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AU - Maeda, Yoshiaki

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AB - 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.

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Smooth *-algebras

Abstract

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