Short history of signed exceptional sequences
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914401056980992 |
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| author | Igusa, Kiyoshi Todorov, Gordana |
| author_facet | Igusa, Kiyoshi Todorov, Gordana |
| contents | Whereas exceptional sequences have a long history with many well-known connections to combinatorics, signed exceptional sequences are relatively recent. The authors introduced this concept in 2017 [19], although it was retroactively realized that the category of noncrossing partitions [24] is a special case of this construction. Buan and Marsh [4] have introduced the concept of $τ$-exceptional sequences to generalize the definitions and theorems to all finite dimensional algebras. This short paper is the story of the original concept of signed exceptional sequences for hereditary algebras and how it developed out of the two authors' study of algebraic K-theory, link invariants, and cluster combinatorics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10910 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Short history of signed exceptional sequences Igusa, Kiyoshi Todorov, Gordana Representation Theory Combinatorics 16G20, 20F55 Whereas exceptional sequences have a long history with many well-known connections to combinatorics, signed exceptional sequences are relatively recent. The authors introduced this concept in 2017 [19], although it was retroactively realized that the category of noncrossing partitions [24] is a special case of this construction. Buan and Marsh [4] have introduced the concept of $τ$-exceptional sequences to generalize the definitions and theorems to all finite dimensional algebras. This short paper is the story of the original concept of signed exceptional sequences for hereditary algebras and how it developed out of the two authors' study of algebraic K-theory, link invariants, and cluster combinatorics. |
| title | Short history of signed exceptional sequences |
| topic | Representation Theory Combinatorics 16G20, 20F55 |
| url | https://arxiv.org/abs/2509.10910 |