Smooth *-algebras
Dubois-Violette, Michel ; Kriegl, Andreas ; Maeda, Yoshiaki ; Michor, Peter W.
HAL, hal-00013424 / Harvested from HAL
Text on HAL
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.
Publié le : 2001-07-05
Classification:  [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA],  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],  [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph],  [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG] 
@article{hal-00013424,
     author = {Dubois-Violette, Michel and Kriegl, Andreas and Maeda, Yoshiaki and Michor, Peter W.},
     title = {Smooth *-algebras},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00013424}
}

Dubois-Violette, Michel; Kriegl, Andreas; Maeda, Yoshiaki; Michor, Peter W. Smooth *-algebras. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00013424/