Finitely presented simple modules over Leavitt path algebras

By P. Ara, Kulumani M. Rangaswamy. 2013

65 citations recorded by the source corpus.

Let $E$ be an arbitrary graph and $K$ be any field. We construct various classes of non-isomorphic simple modules over the Leavitt path algebra $L_{K}(E)$ induced by vertices which are infinite emiters, closed paths which are exclusive cycles and paths which are infinite, and call these simple modules Chen modules. It is shown that every primitive ideal of $L_{K}(E)$ can be realized as the annihilator ideal of some Chen module. Our main result establishes the equivalence between a graph theoretic condition and various conditions concerning the structure of simple modules over $L_K(E)$.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0dd0867266c3bd356433865d9564d88438e37bb7

How researchers see this paper

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In Algebra and Number Theory

1. Roozbeh Hazrat
2. Huanhuan Li
3. P. Ara
4. Aidan Sims
5. G. Abrams
6. Alexei Stepanov
7. Trent Yeend
8. Nikolai Vavilov

In Geometry and Topology

1. Roozbeh Hazrat
2. Huanhuan Li
3. P. Ara
4. Aidan Sims
5. Alexei Stepanov
6. Nikolai Vavilov
7. A. Bak
8. Ben Steinberg

In Mathematical Physics

1. Roozbeh Hazrat
2. Huanhuan Li
3. P. Ara
4. Aidan Sims
5. G. Abrams
6. Trent Yeend
7. M. Tomforde
8. R. Exel

Citations in the corpus

• Graded Steinberg algebras and their representations (2017, methodology): “These representations were further explored in a series of papers [Abrams et al. 2015; Ara and Rangaswamy 2014; 2015; Hazrat and Rangaswamy 2016; Rangaswamy 2016].”