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

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).
112
6
1002
1018
Scherotzke, S.; Sibilla, N.
File in questo prodotto:
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.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/117719
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 4
social impact