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- Publisher Website: 10.1016/j.jalgebra.2015.09.013
- Scopus: eid_2-s2.0-84943572966
- WOS: WOS:000365376700013
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Article: The Hall module of an exact category with duality
Title | The Hall module of an exact category with duality |
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Authors | |
Keywords | Representations of quivers Hall algebras Quantum groups |
Issue Date | 2016 |
Publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra |
Citation | Journal of Algebra, 2016, v. 446, p. 291-322 How to Cite? |
Abstract | We construct from a finitary exact category with duality a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure of . We study in detail Hall modules arising from the representation theory of a quiver with involution. In this case we show that the Hall module is naturally a module over the specialized reduced σ-analogue of the quantum Kac–Moody algebra attached to the quiver. For finite type quivers, we explicitly determine the decomposition of the Hall module into irreducible highest weight modules. |
Persistent Identifier | http://hdl.handle.net/10722/255658 |
ISSN | 2023 Impact Factor: 0.8 2023 SCImago Journal Rankings: 1.023 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Young, MB | - |
dc.date.accessioned | 2018-07-10T08:12:42Z | - |
dc.date.available | 2018-07-10T08:12:42Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Journal of Algebra, 2016, v. 446, p. 291-322 | - |
dc.identifier.issn | 0021-8693 | - |
dc.identifier.uri | http://hdl.handle.net/10722/255658 | - |
dc.description.abstract | We construct from a finitary exact category with duality a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure of . We study in detail Hall modules arising from the representation theory of a quiver with involution. In this case we show that the Hall module is naturally a module over the specialized reduced σ-analogue of the quantum Kac–Moody algebra attached to the quiver. For finite type quivers, we explicitly determine the decomposition of the Hall module into irreducible highest weight modules. | - |
dc.language | eng | - |
dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra | - |
dc.relation.ispartof | Journal of Algebra | - |
dc.subject | Representations of quivers | - |
dc.subject | Hall algebras | - |
dc.subject | Quantum groups | - |
dc.title | The Hall module of an exact category with duality | - |
dc.type | Article | - |
dc.identifier.email | Young, MB: mbyoung@hku.hk | - |
dc.identifier.doi | 10.1016/j.jalgebra.2015.09.013 | - |
dc.identifier.scopus | eid_2-s2.0-84943572966 | - |
dc.identifier.hkuros | 235646 | - |
dc.identifier.volume | 446 | - |
dc.identifier.spage | 291 | - |
dc.identifier.epage | 322 | - |
dc.identifier.isi | WOS:000365376700013 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0021-8693 | - |