Noncommutative projective curves and quantum loop algebras

2002/05/25 by Olivier Schiffmann, Schiffmann, Olivier · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA #math.RA

paper · pdf · doi:10.48550/arxiv.math/0205267

Latex, 40 pages, 2 figures, analog of Kac's conjecture added; final version to appear

arxiv created 2003/02/10 · arxiv updated 2009/11/30

Abstract

We generalize a theorem of Kapranov by showing that the Hall algebra of the category of coherent sheaves on a weighted projective line (over a finite field) provides a realization of the (quantized) enveloping algebra of a certain nilpotent subalgebra of the affinization of the correponding Kac-Moody algebra. In particular this yieds a geometric realization of the quantized enveloping algebra of 2-toroidal (or elliptic) algebras of types D₄, E₆, E₇ or E₈ in terms of weighted projective lines of genus one.

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• The Deligne-Simpson Problem
• Higher S-dualities and Shephard-Todd groups

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