A counterexample to a Gröbner approach for noetherianity of the twisted commutative algebra $\mathrm{Sym}({\mathrm{Sym}}^2({\mathbf{C}}^{\infty }))$

Abstract

We resolve an open question posed by the authors of arXiv:1501.06925v2 in 2015 concerning a Gröbner theoretic approach for the noetherianity of the twisted commutative algebra $\mathrm{Sym}({\mathrm{Sym}}^2({\mathbf{C}}^{\infty }))$. We provide a negative answer to their question by producing an explicit antichain. In doing so, we establish a connection to well studied posets of graphs under the subgraph and induced subgraph relation. We then analyze this connection to suggest future paths of investigation, for example a deeper study of initial ideals in twisted commutative algebras.

22 pages, comments welcome

References in corpus (1)

• Introduction to twisted commutative algebras