Non-zero-divisor conjecture for Vogel's algebra Lambda

Let $\Lambda$ be the graded commutative algebra formed from the antisymmetric subspace of connected tri-/univalent graphs with three labeled univalent vertices, and let $\Lambda_0$ be the subalgebra generated by $x_n$ for $n\geq 1$, with $x_1:=2t$ and $x_2:=t^2$. Non-zero-divisor conjecture. The map

$$\Lambda_0\longrightarrow\Lambda_0,\qquad \lambda\longmapsto t\lambda$$

is injective. Equivalently, $t$ is not a zero divisor in $\Lambda_0$. This assumption is used in the paper to obtain structural information about $\Lambda_0$, including a basis and an embedding into a subring of ${\mathbf{Z}}[t,u,v]$; the source gives no resolution.