Geometric realizations of Ringel-Hall algebras of continuous quivers of type $A$
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914172479995904 |
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| author | Zhao, Minghui |
| author_facet | Zhao, Minghui |
| contents | Lusztig introduced the geometric realizations of quantum groups associated to finite quivers and defined their canonical bases. Sala and Schiffmann introduced the Ringel-Hall algebra of line and realized it as the direct limit of Ringel-Hall algebras of finite quivers of type $A$. In this paper, we shall give geometric realizations of Ringel-Hall algebras of continuous quivers of type $A$ via the geometric realizations of Lusztig by using the method of approximation given by Sala and Schiffmann. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric realizations of Ringel-Hall algebras of continuous quivers of type $A$ Zhao, Minghui Representation Theory Quantum Algebra 16G20, 17B37 Lusztig introduced the geometric realizations of quantum groups associated to finite quivers and defined their canonical bases. Sala and Schiffmann introduced the Ringel-Hall algebra of line and realized it as the direct limit of Ringel-Hall algebras of finite quivers of type $A$. In this paper, we shall give geometric realizations of Ringel-Hall algebras of continuous quivers of type $A$ via the geometric realizations of Lusztig by using the method of approximation given by Sala and Schiffmann. |
| title | Geometric realizations of Ringel-Hall algebras of continuous quivers of type $A$ |
| topic | Representation Theory Quantum Algebra 16G20, 17B37 |
| url | https://arxiv.org/abs/2511.22051 |