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# Lattices of ideals in graph algebras: refining the join operation

thesis
posted on 2022-04-29, 04:12 authored by McDougall, Phoebe

We consider the ideal structure of Leavitt path algebras of graphs that satisfy Condition (K) over commutative rings with identity. The approach we use takes advantage of the relationship between Leavitt path algebras and Steinberg algebras of boundary path groupoids. We establish a lattice $\mathcal{F}'$ consisting of particular maps $\tau:E^0\to \LR$ and show that this lattice is isomorphic to the lattice of ideals of $L_R(E)$. The advantage to our approach over previous lattice isomorphisms, even in the case that $R$ is a field, is that we obtain convenient join and meet operations in $\mathcal{F}'$. Lastly, we provide three concrete examples.

2022-04-29

2022-04-29

## Publisher

Te Herenga Waka—Victoria University of Wellington

CC BY-NC-SA 4.0

Mathematics

## Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Masters

## Degree Name

Master of Science

## ANZSRC Type Of Activity code

1 Pure basic research

## Victoria University of Wellington Item Type

Awarded Research Masters Thesis

en_NZ

## Victoria University of Wellington School

School of Mathematics and Statistics