EVERY GRADED IDEAL OF A LEAVITT PATH ALGEBRA IS <i>GRADED</i> ISOMORPHIC TO A LEAVITT PATH ALGEBRA

Abstract We show that every graded ideal of a Leavitt path algebra is isomorphic to algebra. It known I the graph, as generalised hedgehog which defined based on certain sets vertices uniquely determined by . However, this isomorphism may not be graded. replacing short ‘spines’ graph with possibly fewer, but then necessarily longer spines, we obtain (which call porcupine graph) whose Our proof can adapted that, for closed gauge-invariant J $C^*$ -algebra, there $*$ -isomorphism mapping -algebra onto $J.$