The cones of g-vectors
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917904702767104 |
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| author | Haerizadeh, Mohamad Yassemi, Siamak |
| author_facet | Haerizadeh, Mohamad Yassemi, Siamak |
| contents | This paper studies the wall and chamber structure of algebras via generic decompositions of g-vectors. Specifically, we examine points outside the chambers of the wall and chamber structure of ($τ$-tilting infinite) finite-dimensional algebras. We demonstrate that the cones of g-vectors are both rational and simplicial. Moreover, we show that the open cone of a given g-vector and the interior of its TF-equivalence class coincide if and only if they are of the same dimension. Furthermore, we establish that g-vectors satisfy the ray condition when sufficiently far from the origin. These results allow us to generalize several findings by Asai and Iyama regarding TF-equivalence classes of g-vectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15822 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The cones of g-vectors Haerizadeh, Mohamad Yassemi, Siamak Representation Theory This paper studies the wall and chamber structure of algebras via generic decompositions of g-vectors. Specifically, we examine points outside the chambers of the wall and chamber structure of ($τ$-tilting infinite) finite-dimensional algebras. We demonstrate that the cones of g-vectors are both rational and simplicial. Moreover, we show that the open cone of a given g-vector and the interior of its TF-equivalence class coincide if and only if they are of the same dimension. Furthermore, we establish that g-vectors satisfy the ray condition when sufficiently far from the origin. These results allow us to generalize several findings by Asai and Iyama regarding TF-equivalence classes of g-vectors. |
| title | The cones of g-vectors |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2501.15822 |