Minimal faithful representations of reductive Lie algebras

2007/03/22 by Dietrich Burde, Burde, Dietrich, Wolfgang Moens +1
Mathematics · #17B10 #17B20 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B10 #msc:17B20

paper · pdf · doi:10.48550/arxiv.math/0703657

arxiv created 2007/03/22 · arxiv updated 2009/12/01

Abstract

We prove an explicit formula for the invariant μ(\Lg) for finite-dimensional semisimple, and reductive Lie algebras \Lg over \C. Here μ(\Lg) is the minimal dimension of a faithful linear representation of \Lg. The result can be used to study Dynkin's classification of maximal reductive subalgebras of semisimple Lie algebras.

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