Every graded ideal of a Leavitt path algebra is graded isomorphic to a Leavitt path algebra
Abstract
We show that every graded ideal of a Leavitt path algebra is graded isomorphic to a Leavitt path algebra. It is known that a graded ideal of a Leavitt path algebra is isomorphic to the Leavitt path algebra of a graph, known as the generalized hedgehog graph, which is defined based on certain sets of vertices uniquely determined by . However, this isomorphism may not be graded. We show that replacing the short "spines" of the generalized hedgehog graph with possibly fewer, but then necessarily longer spines, we obtain a graph (which we call the porcupine graph) such that its Leavitt path algebra is graded isomorphic to . Our proof adapts to show that for every closed gauge-invariant ideal of a graph -algebra, there is a gauge-invariant -isomorphism mapping the graph -algebra of the porcupine graph of onto
Keywords
Cite
@article{arxiv.2106.14828,
title = {Every graded ideal of a Leavitt path algebra is graded isomorphic to a Leavitt path algebra},
author = {Lia Vas},
journal= {arXiv preprint arXiv:2106.14828},
year = {2022}
}