On degenerations and extensions of symplectic and orthogonal quiver representations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866909582558756864 |
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| author | Boos, Magdalena Irelli, Giovanni Cerulli |
| author_facet | Boos, Magdalena Irelli, Giovanni Cerulli |
| contents | We discuss degenerations of symplectic and orthogonal representations of symmetric quivers and algebras with self-dualities. As in the non-symmetric case, we define a partial ordering, that we call symmetric Ext-order which gives a sufficient criterion for a symmetric degeneration. Then a detailed discussion of type A quivers and their (symmetric) representation theory via Auslander-Reiten theory leads to our main theorem which states that the symmetric degeneration order of a symmetric quiver of finite type is induced by the usual degeneration order between representations of the underlying quiver. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_08666 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On degenerations and extensions of symplectic and orthogonal quiver representations Boos, Magdalena Irelli, Giovanni Cerulli Representation Theory Algebraic Geometry 16Gxx, 14L35, 17B45 We discuss degenerations of symplectic and orthogonal representations of symmetric quivers and algebras with self-dualities. As in the non-symmetric case, we define a partial ordering, that we call symmetric Ext-order which gives a sufficient criterion for a symmetric degeneration. Then a detailed discussion of type A quivers and their (symmetric) representation theory via Auslander-Reiten theory leads to our main theorem which states that the symmetric degeneration order of a symmetric quiver of finite type is induced by the usual degeneration order between representations of the underlying quiver. |
| title | On degenerations and extensions of symplectic and orthogonal quiver representations |
| topic | Representation Theory Algebraic Geometry 16Gxx, 14L35, 17B45 |
| url | https://arxiv.org/abs/2106.08666 |