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

Gene Abrams; Roozbeh Hazrat

doi:10.1007/s40879-023-00613-4

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

Gene Abrams, Roozbeh Hazrat

Western Sydney University

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In our main result, we establish that any conical sandpile monoid M= SP (E) of a directed sandpile graph E can be realised as the V-monoid of a weighted Leavitt path algebra Lk(F, w) (where F is an explicitly constructed subgraph of E), and consequently, the sandpile group G(E) is realised as the Grothendieck group K(Lk(F, w)). Additionally, we describe the conical sandpile monoids which arise as the V-monoid of a standard (i.e., unweighted) Leavitt path algebra.

Original language	English
Article number	21
Number of pages	28
Journal	European Journal of Mathematics
Volume	9
Issue number	2
DOIs	https://doi.org/10.1007/s40879-023-00613-4
Publication status	Published - Jun 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Notes

WIP in RD

Keywords

Grothendieck group
Sandpile monoid
Abelian sandpile model
Weighted Leavitt path algebra

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10.1007/s40879-023-00613-4

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abstract = "In our main result, we establish that any conical sandpile monoid M= SP (E) of a directed sandpile graph E can be realised as the V-monoid of a weighted Leavitt path algebra Lk(F, w) (where F is an explicitly constructed subgraph of E), and consequently, the sandpile group G(E) is realised as the Grothendieck group K(Lk(F, w)). Additionally, we describe the conical sandpile monoids which arise as the V-monoid of a standard (i.e., unweighted) Leavitt path algebra.",

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AU - Abrams, Gene

AU - Hazrat, Roozbeh

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N2 - In our main result, we establish that any conical sandpile monoid M= SP (E) of a directed sandpile graph E can be realised as the V-monoid of a weighted Leavitt path algebra Lk(F, w) (where F is an explicitly constructed subgraph of E), and consequently, the sandpile group G(E) is realised as the Grothendieck group K(Lk(F, w)). Additionally, we describe the conical sandpile monoids which arise as the V-monoid of a standard (i.e., unweighted) Leavitt path algebra.

AB - In our main result, we establish that any conical sandpile monoid M= SP (E) of a directed sandpile graph E can be realised as the V-monoid of a weighted Leavitt path algebra Lk(F, w) (where F is an explicitly constructed subgraph of E), and consequently, the sandpile group G(E) is realised as the Grothendieck group K(Lk(F, w)). Additionally, we describe the conical sandpile monoids which arise as the V-monoid of a standard (i.e., unweighted) Leavitt path algebra.

KW - Grothendieck group

KW - Sandpile monoid

KW - Abelian sandpile model

KW - Weighted Leavitt path algebra

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M3 - Article

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SN - 2199-675X

VL - 9

JO - European Journal of Mathematics

JF - European Journal of Mathematics

IS - 2

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ER -

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

Abstract

Bibliographical note

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Keywords

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