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SIMPLICITY OF LEAVITT PATH ALGEBRAS VIA GRADED RING THEORY
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Journal Article
SIMPLICITY OF LEAVITT PATH ALGEBRAS VIA GRADED RING THEORY
2023
Overview
Suppose that R is an associative unital ring and that
$E=(E^0,E^1,r,s)$
is a directed graph. Using 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 centre of a simple Leavitt path algebra.
Publisher
Cambridge University Press
Subject
