descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Apr 2001Embargo end date: 01 Jan 2000 English Publisher:Springer Science and Business Media LLCJournal:Selecta Mathematica, volume 7, pages 1-56 (issn: 1022-1824, eissn: 1420-9020,

Authors: Frenkel, Igor; Malkin, Anton; Vybornov, Maxim;

doi: 10.1007/pl00001397 , 10.48550/arxiv.math/0005119

arXiv: math/0005119

Affine Lie algebras and tame quivers

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Abstract

C.M. Ringel defined Hall algebra associated with the category of representations of a quiver of Dynkin type and gave an explicit description of the structure constants of the corresponding Lie algebra. We utilize functorial properties of the Hall algebra to give a simple proof of Ringel's result, and to generalize it to the case of a quiver of affine type.

48 pages

Related Organizations

Yale University
United States
Massachusetts Institute of Technology
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Duke University
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Keywords

reflection functors, quantized enveloping algebras, Hall algebras, Hopf algebras (associative rings and algebras), Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, FOS: Mathematics, Representations of quivers and partially ordered sets, representations of quivers, affine Lie algebras, Representation Theory (math.RT), Mathematics - Representation Theory

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