The composition algebra of an affine quiver

2004/03/12 by Andrew Hubery, Hubery, Andrew · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA #math.RT #msc:16G20 #msc:17B37

paper · pdf · doi:10.48550/arxiv.math/0403206

arxiv created 2004/03/12 · arxiv updated 2009/12/01

Abstract

We study the Hall and composition algebras of an affine quiver. In the case of a cyclic quiver, we provide generators for the central polynomial algebra described by Schiffmann and prove that this is in fact the whole of the centre of the Hall algebra. For an affine quiver without oriented cycles, we obtain a structure theorem for the composition algebra refining the structure provided by Zhang.

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• Two descriptions of the quantum affine algebra U_v(\mathfraksl₂) via Hall algebra approach

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