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arXiv · 2603.25134

Leavitt path algebras having Graded Invariant Basis Number

Ngo Tan Phuc
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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.

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Ngo Tan Phuc. 2026-03-26. Leavitt path algebras having Graded Invariant Basis Number. https://arxiv.org/abs/2603.25134

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