Additive Polynomials for Finite Groups of Lie Type

Details Additive Polynomials for Finite Groups of Lie Type Additive Polynomials for Finite Groups of Lie Type

2009-06-07

arxiv.org/abs/0906.1380v3

Mathematics

Group Theory

59 pages; v2: added reference, slightly restructured section 6.1, few small rewordings; v3: completed realization of Steinberg

Scientific paper

This paper provides a realization of all classical and most exceptional finite groups of Lie type as Galois groups over function fields over F_q and derives explicit additive polynomials for the extensions. Our unified approach is based on results of Matzat which give bounds for Galois groups of Frobenius modules and uses the structure and representation theory of the corresponding connected linear algebraic groups.

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