Abstract. We consider a generalization $\star_\alpha $ of the fundamental star product built by Kontsevich $\star_\alpha^K$ for linear structures $\alpha$. We study closeness and relativity of these star products and we prove that the only Kontsevich star product strict and relative is $\star_\alpha^K$.

AMS Subject Classification (1991): 16S80, 16E40, 17B35

Keyword(s): Deformation quantization, star products

Received November 4, 2003. (Registered under 5850/2009.)