In this paper, we give a geometric construction of the quantum group Ut(G) using Nakajima categories, which were developed in Scherotzke ('Quiver varieties and self-injective algebras', Preprint, 2014, arxiv.org/abs/1405.4729). Our methods allow us to establish a direct connection between the algebraic realization of the quantum group as Hall algebra by Bridgeland ('Quantum groups via Hall algebras of complexes', Annals of Maths. 177 (2013) 739-759) and its geometric counterpart by Qin ('Quantum groups via cyclic quiver varieties I', Compos. Math., Preprint, 2013, arxiv.org/abs/1312.1101).
Quiver varieties and Hall algebras / Scherotzke, S.; Sibilla, N.. - In: PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6115. - 112:6(2016), pp. 1002-1018. [10.1112/plms/pdw016]
Quiver varieties and Hall algebras
Sibilla N.
2016-01-01
Abstract
In this paper, we give a geometric construction of the quantum group Ut(G) using Nakajima categories, which were developed in Scherotzke ('Quiver varieties and self-injective algebras', Preprint, 2014, arxiv.org/abs/1405.4729). Our methods allow us to establish a direct connection between the algebraic realization of the quantum group as Hall algebra by Bridgeland ('Quantum groups via Hall algebras of complexes', Annals of Maths. 177 (2013) 739-759) and its geometric counterpart by Qin ('Quantum groups via cyclic quiver varieties I', Compos. Math., Preprint, 2013, arxiv.org/abs/1312.1101).| File | Dimensione | Formato | |
|---|---|---|---|
|
hall algebras quiver varieties.pdf
non disponibili
Tipologia:
Versione Editoriale (PDF)
Licenza:
Non specificato
Dimensione
225.04 kB
Formato
Adobe PDF
|
225.04 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
