Higher homological algebra for one-point extensions of bipartite hereditary algebras and spectral graph theory
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929571887054848 |
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| author | Jacobsen, Karin M. Sandøy, Mads Hustad Vaso, Laertis |
| author_facet | Jacobsen, Karin M. Sandøy, Mads Hustad Vaso, Laertis |
| contents | In this article we study higher homological properties of $n$-levelled algebras and connect them to properties of the underlying graphs. Notably, to each $2$-representation-finite quadratic monomial algebra $Λ$ we associate a bipartite graph $\overline{B_Λ}$ and we classify all such algebras $Λ$ for which $\overline{B_Λ}$ is regular or edge-transitive. We also show that if $\overline{B_Λ}$ is semi-regular, then it is a reflexive graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00470 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher homological algebra for one-point extensions of bipartite hereditary algebras and spectral graph theory Jacobsen, Karin M. Sandøy, Mads Hustad Vaso, Laertis Representation Theory Combinatorics 16G20, 16E65, 16S37, 05C25 In this article we study higher homological properties of $n$-levelled algebras and connect them to properties of the underlying graphs. Notably, to each $2$-representation-finite quadratic monomial algebra $Λ$ we associate a bipartite graph $\overline{B_Λ}$ and we classify all such algebras $Λ$ for which $\overline{B_Λ}$ is regular or edge-transitive. We also show that if $\overline{B_Λ}$ is semi-regular, then it is a reflexive graph. |
| title | Higher homological algebra for one-point extensions of bipartite hereditary algebras and spectral graph theory |
| topic | Representation Theory Combinatorics 16G20, 16E65, 16S37, 05C25 |
| url | https://arxiv.org/abs/2411.00470 |