  Let $G$ be the Lie group $SO_e(4,1)$, with maximal compact subgroup $K =
S(O(4) \times O(1))_e\cong SO(4)$. Let
$\mathfrak{g}=\mathfrak{so}(5,\mathbb{C})$ be the complexification of the Lie
algebra $\mathfrak{g}_0 = \mathfrak{so}(4,1)$ of $G$, and let $U(\mathfrak{g})$
be the universal enveloping algebra of $\mathfrak{g}$. Let $\mathfrak{g} =
\mathfrak{k} \oplus \mathfrak{p}$ be the Cartan decomposition of
$\mathfrak{g}$, and $C(\mathfrak{p})$ the Clifford algebra of $\mathfrak{p}$
with respect to the trace form $B(X, Y) = \text{tr}(XY)$ on $\mathfrak{p}$. In
this paper we give explicit generators of the algebra $(U(\mathfrak{g}) \otimes
C(\mathfrak{p}))^{K}$.
