Smooth *-algebras

2001/06/30 by Michel Dubois-Violette, Andreas Kriegl, Yoshiaki Maeda +1
Mathematics · Physics and Astronomy · #math.QA #math-ph #math.MP #math.SG #msc:46L87 #msc:46L60

paper · pdf

published as Progress of Theoretical Physics Supplement Number 144 (2001), 54-78. · 25 pages; Author names corrected

arxiv created 2001/07/13 · arxiv updated 2009/11/30

Abstract

Looking for the universal covering of the smooth non-commutative torus leads to a curve of associative multiplications on the space \Cal O_M'(\Bbb R²ⁿ)≅ \Cal O_C(\Bbb R²ⁿ) of Laurent Schwartz which is smooth in the deformation parameter ℏ. The Taylor expansion in ℏ leads to the formal Moyal star product. The non-commutative 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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