An antichain of monomial ideals in a twisted commutative algebra

Laudone, Robert

doi:10.1090/proc/16751

An antichain of monomial ideals in a twisted commutative algebra
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by Robert P. Laudone;

Proc. Amer. Math. Soc. 152 (2024), 2297-2316

DOI: https://doi.org/10.1090/proc/16751

Published electronically: April 18, 2024

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Abstract:

We resolve an open question posed by Nagpal, Sam and Snowden [Selecta. Math. (N.S.) 22 (2016), pp. 913–937] in 2015 concerning a Gröbner theoretic approach to the noetherianity of the twisted commutative algebra $Sym(Sym^2(\mathbf {C}^\infty ))$. 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.

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