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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.07328 |
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| _version_ | 1866916587178557440 |
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| author | Haerizadeh, Mohamad Yassemi, Siamak |
| author_facet | Haerizadeh, Mohamad Yassemi, Siamak |
| contents | The non-decreasing condition on g-vectors is introduced. Our study shows that this condition is both necessary and sufficient to ensure that the generically indecomposable direct summands of a given g-vector are linearly independent. Additionally, we prove that for any finite dimensional algebra $Λ$, under the non-decreasing condition, the number of generically indecomposable irreducible components that appear in the decomposition of a given generically $τ$-reduced component is lower than or equal to $|Λ|$. This solves the conjecture concerning the cardinality of component clusters by Cerulli-Labardini-Schröer, in a reasonable generality. Lastly, we study numerical criteria to check the wildness of g-vectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07328 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The non-decreasing condition on g-vectors Haerizadeh, Mohamad Yassemi, Siamak Representation Theory The non-decreasing condition on g-vectors is introduced. Our study shows that this condition is both necessary and sufficient to ensure that the generically indecomposable direct summands of a given g-vector are linearly independent. Additionally, we prove that for any finite dimensional algebra $Λ$, under the non-decreasing condition, the number of generically indecomposable irreducible components that appear in the decomposition of a given generically $τ$-reduced component is lower than or equal to $|Λ|$. This solves the conjecture concerning the cardinality of component clusters by Cerulli-Labardini-Schröer, in a reasonable generality. Lastly, we study numerical criteria to check the wildness of g-vectors. |
| title | The non-decreasing condition on g-vectors |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2401.07328 |