On the Gauss algebra of toric algebras
J\"urgen Herzog, Raheleh Jafari, Abbas Nasrollah Nejad

TL;DR
This paper investigates the structure and generators of the Gauss algebra associated with certain monomial-generated subalgebras of polynomial rings, providing explicit descriptions for specific classes like Borel fixed and Veronese algebras.
Contribution
It characterizes the generators and structure of the Gauss algebra for various classes of monomial algebras, including Borel fixed, squarefree Veronese, and edge rings of bipartite graphs.
Findings
Generators of $ ext{GG}(A)$ are monomials of degree $(r-1)d$.
Explicit descriptions of $ ext{GG}(A)$ for Borel fixed and Veronese algebras.
Embedding dimension of $ ext{GG}(A)$ for bipartite graphs with loops is bounded by graph complexity.
Abstract
Let be a -subalgebra of the polynomial ring of dimension , generated by finitely many monomials of degree . Then the Gauss algebra of is generated by monomials of degree in . We describe the generators and the structure of , when is a Borel fixed algebra, a squarefree Veronese algebra, generated in degree , or the edge ring of a bipartite graph with at least one loop. For a bipartite graph with one loop, the embedding dimension of is bounded by the complexity of the graph .
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