Construction of Certain Semi-Simple Groups*
- 1 January 1964
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 16, 490-508
- https://doi.org/10.4153/cjm-1964-051-6
Abstract
In (3), Chevalley constructed, for every field K and every semi-simple Lie algebra g over the complex number field, a group GK(g) by using a system of root vectors Xr which satisfies a certain condition (more precisely, (1.2) in Section 1). The main point of Chevalley's construction lies in the fact that the above-mentioned root vectors furnish a basis of g such that, for every root r, exp(t ad Xr) is represented by a matrix (Aij(t)) whose entries Aij(t) are polynomials in t with integral coefficients.Keywords
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