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arXiv · 2606.17715

Duality of monoids up to symmetry

Dinh Van Le·Tim Römer·Nguyen Thi Vien
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Abstract

We study duality for monoids in an infinite-dimensional setting that are invariant under the action of the infinite symmetric group Sym. Our main result is an equivariant Minkowski--Weyl theorem for monoids. More precisely, we analyze the evolution of dual monoids along stabilizing Sym-invariant chains and describe the eventual behavior of their equivariant Hilbert bases. In addition, we develop a systematic study of structural properties of dual symmetric monoids, including a characterization of the duals of positive and non-positive monoids.

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Dinh Van Le, Tim Römer, Nguyen Thi Vien. 2026-06-16. Duality of monoids up to symmetry. https://arxiv.org/abs/2606.17715

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