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arXiv · 2510.16638

Root monoids and active algebraic groups

Ekaterina Nistiuk·Yulia Zaitseva
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Abstract

We describe affine monoids whose group of invertible elements is an active semidirect product of a unipotent group and a torus, in terms of comultiplications on the algebra of regular functions. We introduce the notion of a root monoid, which is constructed from a set of Demazure root pairs on an affine toric variety, and study the properties of such monoids.

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Ekaterina Nistiuk, Yulia Zaitseva. 2025-10-18. Root monoids and active algebraic groups. https://arxiv.org/abs/2510.16638

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