  We demonstrate a method for finding the decoherence-subalgebra
$\mathcal{N}(\mathcal{T})$ of a Gaussian quantum Markov semigroup on the von
Neumann algebra $\mathcal{B}(\Gamma(\mathbb{C}^d))$ of all bounded operator on
the Fock space $\Gamma(\mathbb{C}^d)$ on $\mathbb{C}^d$. We show that
$\mathcal{N}(\mathcal{T})$ is a type I von Neumann algebra
$L^\infty(\mathbb{R}^{d_c};\mathbb{C})\bar{\otimes}\mathcal{B}(\Gamma(\mathbb{C}^{d_f}))$
determined, up to unitary equivalence, by two natural numbers $d_c,d_f\leq d$.
This result is illustrated by some applications and examples.
