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Paper   IPM / M / 15510
School of Mathematics
  Title:   On the Gauss algebra of toric algebras
  Author(s):  Raheleh Jafari (Joint with J. Herzog and A. Nasrollah Nejad)
  Status:   Published
  Journal: J. Algebraic Combin.
  Vol.:  51
  Year:  2020
  Pages:   1-17
  Supported by:  IPM
Let A be a K-subalgebra of the polynomial ring S=K[x1,�?�,xd] 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.

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