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arXiv · 2112.09218

Connections between Abelian sandpile models and the $K$-theory of weighted Leavitt path algebras

Gene Abrams·Roozbeh Hazrat
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Abstract

In our main result, we establish that any conical sandpile monoid $M = SP(G)$ of a directed sandpile graph $G$ can be realised as the $\mathcal{V}$-monoid of a weighted Leavitt path algebra $L_K(E,w)$, and consequently, the sandpile group as the Grothendieck group $K_0(L_K(E,w))$. We show how to explicitly construct $(E,w)$ from $G$. Additionally, we describe the conical sandpile monoids which arise as the $\mathcal{V}$-monoid of a standard (i.e., unweighted) Leavitt path algebra.

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Gene Abrams, Roozbeh Hazrat. 2021-12-16. Connections between Abelian sandpile models and the $K$-theory of weighted Leavitt path algebras. https://arxiv.org/abs/2112.09218

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