Leavitt path algebras having Graded Invariant Basis Number
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908915490357248 |
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| author | Phuc, Ngo Tan |
| author_facet | Phuc, Ngo Tan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_25134 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Leavitt path algebras having Graded Invariant Basis Number Phuc, Ngo Tan Rings and Algebras 16S88, 16S99, 05C25 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. |
| title | Leavitt path algebras having Graded Invariant Basis Number |
| topic | Rings and Algebras 16S88, 16S99, 05C25 |
| url | https://arxiv.org/abs/2603.25134 |