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Smooth *-algebras

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

Looking for the universal covering of the smooth non-commutative torus leads to a curve of associative multiplications on the space $\Cal O_M'(\Bbb R^{2n})\cong \Cal O_C(\Bbb R^{2n})$ of Laurent Schwartz which is smooth in the deformation parameter $\hbar$. The Taylor expansion in $\hbar$ 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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BibTeXRIS

Michel Dubois-Violette, Andreas Kriegl, Yoshiaki Maeda, Peter W. Michor. 2001-07-13. Smooth *-algebras. https://arxiv.org/abs/math/0106150

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