Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9518170 | Advances in Mathematics | 2005 | 44 Pages |
Abstract
This article is to study relations between tubular algebras of Ringel and elliptic Lie algebras in the sense of Saito-Yoshii. Using the explicit structure of the derived categories of tubular algebras given by Happel-Ringel, we prove that the elliptic Lie algebra of type D4(1,1), E6(1,1), E7(1,1) or E8(1,1) is isomorphic to the Ringel-Hall Lie algebra of the root category of the tubular algebra with the same type. As a by-product of our proof, we obtain a Chevalley basis of the elliptic Lie algebra following indecomposable objects of the root category of the corresponding tubular algebra. This can be viewed as an analogue of the Frenkel-Malkin-Vybornov theorem in which they described a Chevalley basis for each untwisted affine Kac-Moody Lie algebra by using indecomposable representations of the corresponding affine quiver.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Yanan Lin, Liangang Peng,