Article
| Title: | Two-parameter quantum groups via Hall algebras of complexes (English) |
| Author: | Xia, Limeng |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 3 |
| Year: | 2026 |
| Pages: | 935-946 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We construct the twisted Hall algebra ${\rm H}_{\rm tw}(\mathcal {C}(\mathcal {P}))$ involving $\mathbb {Z}_2$-graded projective complexes of quiver representations. Then we describe two-parameter quantum groups of symmetric Kac-Moody Lie algebras via the localization $\mathcal {DH}(\mathcal {A})$ of ${\rm H}_{\rm tw}(\mathcal {C}(\mathcal {P}))$ with respective to acyclic complexes. For a Dynkin quiver, we realized generic two-parameter quantum groups via corresponding Hall algebras defined by the Ringel-Hall polynomial. (English) |
| Keyword: | two-parameter quantum group |
| Keyword: | quiver |
| Keyword: | complex |
| Keyword: | Hall algebra |
| MSC: | 16G20 |
| MSC: | 17B37 |
| DOI: | 10.21136/CMJ.2026.0453-25 |
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| Date available: | 2026-09-11T13:15:07Z |
| Last updated: | 2026-09-14 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153736 |
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