Smooth *-algebras

Details Smooth *-algebras Smooth *-algebras

2001-06-18

arxiv.org/abs/math/0106150v3

Progress of Theoretical Physics Supplement Number 144 (2001), 54-78.

Mathematics

Quantum Algebra

25 pages; Author names corrected

Scientific paper

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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