On the Gauss Algebra of Toric Algebras

Jürgen Herzog, Raheleh Jafari, Abbas Nasrollah Nejad
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
more » ... dimension of $\GG(A)$ is bounded by the complexity of the graph $G$.
doi:10.14760/owp-2018-07 fatcat:nxdgesbnw5b2rouhxslwjqmdpe