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

2021/12/16 by Gene Abrams, Abrams, Gene, Roozbeh Hazrat +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2112.09218

openalex publication_date 2021/12/16 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

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 V-monoid of a weighted Leavitt path algebra L_K(E,w), and consequently, the sandpile group as the Grothendieck group K₀(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 V-monoid of a standard (i.e., unweighted) Leavitt path algebra.

Cited by

• Embedding K-algebras into Leavitt algebra L_K(1, 2)

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