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arXiv · 2501.07310

Modules determined by their Newton polytopes

Peigen Cao
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Abstract

In the $\tau$-tilting theory, there exist two classes of foundamental modules: indecomposable $\tau$-rigid modules and left finite bricks. In this paper, we prove the indecomposable $\tau$-rigid modules and the left finite bricks are uniquely determined by their Newton polytopes spanned by the dimensional vectors of their quotient modules. This is a kind of generalization of Gabriel's result that the indecomposable modules over path algebras of Dynkin quivers are uniquely determined by their dimensional vectors.

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Peigen Cao. 2025-01-13. Modules determined by their Newton polytopes. https://arxiv.org/abs/2501.07310

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