IJPAM: Volume 2, No. 1 (2002)

TANGENTIAL $\star$-PRODUCT ON
THE DUAL OF NILPOTENT LIE ALGEBRA

Mabrouk Ben Ammar$^1$, Béchir Dali$^2$
Dept. of Mathematics
Faculty of Sciences
University of Sfax
3018, Sfax, TUNISIA
$^1$e-mail: Mabrouk.Ben Ammar@fss.rnu.tn
$^2$e-mail: Bechir.Dali@fss.rnu.tn


Abstract.We consider a nilpotent Lie group $G$ with Lie algebra $\frak g$. We prove that, there exists an invariant polynomial function $B$ such that $U(\frak g)_B$ is isomorphic to $S(\frak g)_B^G \otimes {\mathcal A}_k$, where ${\mathcal A}_k$ is the Weyl algebra spanned by the canonical coordinates of a (generic) coadjoint orbit $\mathcal O$. For such orbit, we construct a global chart in which the tangential $\star$-product defined in [2] coincides with the Moyal product.

Received: May 5, 2002

AMS Subject Classification: 17B45

Key Words and Phrases: Lie algebra, Poisson bracket, $\star$-product, Moyal product

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 2
Issue: 1