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Lattices of ideals in graph algebras: refining the join operation

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posted on 29.04.2022, 04:12 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.

History

Copyright Date

29/04/2022

Date of Award

29/04/2022

Publisher

Te Herenga Waka - Victoria University of Wellington

Rights License

CC BY-NC-SA 4.0

Degree Discipline

Mathematics

Degree Grantor

Te Herenga Waka - Victoria University of Wellington

Degree Level

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

Language

en_NZ

Victoria University of Wellington School

School of Mathematics and Statistics

Advisors

Clark, Lisa