On matrices in prescribed conjugacy classes with no common invariant subspace and sum zero

2001/03/15 by William Crawley-Boevey, Crawley-Boevey, William · 4 citations
Mathematics · #15A24 #16G20 (Primary) 34M50 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AG #math.RA #msc:15A24 #msc:16G20 #msc:34M50

paper · pdf · doi:10.48550/arxiv.math/0103101

11 pages. Only trivial changes since the last version

arxiv created 2002/05/22 · arxiv updated 2009/11/30

Abstract

We determine those k-tuples of conjugacy classes of matrices, from which it is possible to choose matrices which have no common invariant subspace and have sum zero. This is an additive version of the Deligne-Simpson problem. We deduce the result from earlier work of ours on preprojective algebras and the moment map for representations of quivers. Our answer depends on the root system for a Kac-Moody Lie algebra.

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• On the global dimension and Koszul property for preprojective algebras
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