Let $V$ be a finite-dimensional vector space over $\mathbb C$. Define $\bigwedge^{\text{even}}(V) = \bigoplus_{k = 0}^{\lfloor \frac{\dim V}{2} \rfloor} \bigwedge^{2k}(V).$ This is a (finitely generated) commutative subalgebra of the exterior algebra $\bigwedge(V).$
I'm looking for a reference describing $\bigwedge^{\text{even}}(V)$ as a quotient of a polynomial algebra.
You can write it as a quotient of the symmetric algebra on the vector space $\bigwedge^2V$, so the image of the canonical map $$ \phi\colon S^\bullet(\textstyle{\bigwedge^2}V) \to \textstyle{\bigwedge^\bullet}(V). $$
Edit: The relations.
We can write the generators of $S^\bullet(\bigwedge^2V)$ as $x_{ij}$ for $1\leq i<j\leq\dim V$. Then the kernel $I$ of $\phi$ clearly contains the elements $$ x_{ij}x_{kl} = \begin{cases} 0 &\textrm{if }\{i,j\}\cap\{k,l\}\neq\emptyset\\ \pm x_{ab}x_{cd} &\textrm{if }\{i,j\}\cup\{k,l\}=\{a,b,c,d\} \textrm{ with }a<b<c<d \end{cases} $$ (where the signs are taken appropriately).
To see that these are all relations, note that the quotient $S^\bullet(\bigwedge^2V)/I$ is spanned as a vector space by products $x_{a,b}x_{c,d}\cdots x_{e,f}$ with $a<b<c<d<\cdots<e<f$. On the other hand, the images of these elements form a basis for $\bigwedge^{2\bullet}V$.