On the construction of semisimple Lie algebras and Chevalley groups

2016/02/15 by Geck, Meinolf · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1602.04583

Abstract

Let \mathfrakg be a semisimple complex Lie algebra. Recently, Lusztig simplified the traditional construction of the corresponding Chevalley groups (of adjoint type) using the "canonical basis" of the adjoint representation of~\mathfrakg. Here, we present a variation of this idea which leads to a new, and quite elementary construction of~\mathfrakg itself from its root system. An additional feature of this set-up is that it also gives rise to explicit Chevalley bases of \mathfrakg.

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