Leavitt path algebras having Graded Invariant Basis Number
Rings and Algebras
2026-03-27 v1
Abstract
In this paper, we study the Graded Invariant Basis Number (grIBN) property for Leavitt path algebras of finite graphs. Using the talented monoid as our main tool, we establish a complete matrix-theoretic characterization of when a Leavitt path algebra of a finite graph fails to have gr-IBN. Consequently, we identify several classes of graphs whose Leavitt path algebras have gr-IBN, including graphs with sinks, Cayley graphs, and Hopf graphs associated with finite groups. We also investigate the preservation of gr-IBN under quotients by hereditary saturated subsets and under Cartesian products of graphs.
Cite
@article{arxiv.2603.25134,
title = {Leavitt path algebras having Graded Invariant Basis Number},
author = {Ngo Tan Phuc},
journal= {arXiv preprint arXiv:2603.25134},
year = {2026}
}