# The Current Galilei Algebra and Associated Random Variables

### From NZJM

**New Zealand Journal of Mathematics**

**Vol.** 41, (2011), **Pages** 131-142

**Luigi Accardi**

Centro Vito Volterra,

Universita di Roma Tor Vergata

via Columbia 2, 00133 Roma, Italy

mailto:accardi@volterra.mat.uniroma2.it

**Andreas Boukas**

Centro Vito Volterra,

Universita di Roma Tor Vergata

via Columbia 2, 00133 Roma, Italy

mailto:andreasboukas@yahoo.com

**Abstract** We compute the Fock kernel for the one-mode (i.e. restricted to a single interval) and current (i.e. extended to simple functions) Galilei algebra. We also compute the characteristic function of a family of random variables naturally associated with the Galilei algebra.

**Keywords** Galilei algebra, Heisenberg algebra, Central extension, Fock representation, Fock kernel, Renormalized Higher Powers of White Noise

**Classification** (MSC2000) Primary 17B15, 17B56, 60B15, 81S05. Secondary 81R05, 81S25.