  Let $A$ be a $K$-subalgebra of the polynomial ring $S=K[x_1,\ldots,x_d]$ of
dimension $d$, generated by finitely many monomials of degree $r$. Then the
Gauss algebra $\GG(A)$ of $A$ is generated by monomials of degree $(r-1)d$ in
$S$. We describe the generators and the structure of $\GG(A)$, when $A$ is a
Borel fixed algebra, a squarefree Veronese algebra, generated in degree $2$, or
the edge ring of a bipartite graph with at least one loop. For a bipartite
graph $G$ with one loop, the embedding dimension of $\GG(A)$ is bounded by the
complexity of the graph $G$.
