# The DFR-Algebra for Poisson Vector Bundles

January 07, 2012

The aim of the present paper is to present the construction of a general
family of $C^*$-algebras that includes, as a special case, the "quantum
space-time algebra" first introduced by Doplicher, Fredenhagen and Roberts. To
this end, we first review, within the $C^*$-algebra context, the Weyl-Moyal
quantization procedure on a fixed Poisson vector space (a vector space equipped
with a given bivector, which may be degenerate). We then show how to extend
this construction to a Poisson vector bundle over a general manifold $M$,
giving rise to a $C^*$-algebra which is also a module over $C_0(M)$. Apart from
including the original DFR-model, this method yields a "fiberwise quantization"
of general Poisson manifolds.

Keywords:

DFR algebra, poisson vector bundle