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Construction of Certain Semi-Simple Groups*

Published online by Cambridge University Press:  20 November 2018

Rimhak Ree
Rimhak Ree*
Affiliation:
University of British Columbia
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 490 - 508
Copyright
Copyright © Canadian Mathematical Society 1964

References

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