ON THE CONSTRUCTION OF SEMISIMPLE LIE ALGEBRAS AND CHEVALLEY GROUPS.

Let g 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 g. Here, we present a variation of this idea which leads to a new, and quite elementary, construction of g itself from its root system. An additional feature of this set-up is that it also gives rise to explicit Chevalley bases of g. [ABSTRACT FROM AUTHOR]