Simplicity of Leavitt path algebras via graded ring theory

Patrik Lundström; Johan Öinert

Simplicity of Leavitt path algebras via graded ring theory

Rings and Algebras 2022-12-02 v2 Operator Algebras

Authors: Patrik Lundström , Johan Öinert

Abstract

Suppose that $R$ is an associative unital ring and that $E=(E^0,E^1,r,s)$ is a directed graph. Utilizing results from graded ring theory we show, that the associated Leavitt path algebra $L_R(E)$ is simple if and only if $R$ is simple, $E^0$ has no nontrivial hereditary and saturated subset, and every cycle in $E$ has an exit. We also give a complete description of the center of a simple Leavitt path algebra.

Keywords

leavitt path algebra graded ring theory simplicity directed graph center hereditary saturated subset

Cite

@article{arxiv.2211.10233,
  title  = {Simplicity of Leavitt path algebras via graded ring theory},
  author = {Patrik Lundström and Johan Öinert},
  journal= {arXiv preprint arXiv:2211.10233},
  year   = {2022}
}

Comments

10 pages. From v1 to v2: Added references and updated Section 1

Simplicity of Leavitt path algebras via graded ring theory

Abstract

Keywords

Cite

Comments

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