Morphisms and extensions between bricks over preprojective algebras of type A
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909293158072320 |
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| author | Hanson, Eric J. You, Xinrui |
| author_facet | Hanson, Eric J. You, Xinrui |
| contents | The bricks over preprojective algebras of type A are known to be in bijection with certain combinatorial objects called "arcs". In this paper, we show how one can use arcs to compute bases for the Hom-spaces and first extension spaces between bricks. We then use this description to classify the "weak exceptional sequences" over these algebras. Finally, we explain how our result relates to a similar combinatorial model for the exceptional sequences over hereditary algebras of type A. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11513 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Morphisms and extensions between bricks over preprojective algebras of type A Hanson, Eric J. You, Xinrui Representation Theory 16G20, 16G10 The bricks over preprojective algebras of type A are known to be in bijection with certain combinatorial objects called "arcs". In this paper, we show how one can use arcs to compute bases for the Hom-spaces and first extension spaces between bricks. We then use this description to classify the "weak exceptional sequences" over these algebras. Finally, we explain how our result relates to a similar combinatorial model for the exceptional sequences over hereditary algebras of type A. |
| title | Morphisms and extensions between bricks over preprojective algebras of type A |
| topic | Representation Theory 16G20, 16G10 |
| url | https://arxiv.org/abs/2303.11513 |