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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2410.16422 |
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| _version_ | 1866917812351533056 |
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| author | Barrios, Marcos Lanzilotta, Marcelo Mata, Gustavo |
| author_facet | Barrios, Marcos Lanzilotta, Marcelo Mata, Gustavo |
| contents | In [8] V. Gélinas introduced a homological invariant, called {\it delooping level} (dell), that bounds the finitistic dimension. In this article, we introduce another homological invariant (Dell) related to the delooping level for an Artin algebra. We compare this new tool with other dimensions as the finitistic dimension or the $ϕ$-dimension (where $ϕ$ is the first Igusa-Todorov function), and we also generalize Theorem 4.3. from [9] to truncated path algebras (Theorem 4.18). Finally, we show that for a monomial algebra $A$ the difference dell($A$) - Findim($A$) can be arbitrarily large (Example 4.22). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16422 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Delooping levels Barrios, Marcos Lanzilotta, Marcelo Mata, Gustavo Representation Theory In [8] V. Gélinas introduced a homological invariant, called {\it delooping level} (dell), that bounds the finitistic dimension. In this article, we introduce another homological invariant (Dell) related to the delooping level for an Artin algebra. We compare this new tool with other dimensions as the finitistic dimension or the $ϕ$-dimension (where $ϕ$ is the first Igusa-Todorov function), and we also generalize Theorem 4.3. from [9] to truncated path algebras (Theorem 4.18). Finally, we show that for a monomial algebra $A$ the difference dell($A$) - Findim($A$) can be arbitrarily large (Example 4.22). |
| title | Delooping levels |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2410.16422 |