Sharply transitive linear algebraic groups |
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Authors: | Peter Müller |
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Institution: | (1) Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstrasse 1 1/2, D-8520 Erlangen, Germany |
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Abstract: | We study Zariski-closed linear groupsG GL
n
(k) over fieldsk of characteristic 0 which act sharply transitively on the non-zero vectors ofk
n
. For square-freen, orn 15, or ifk has cohomological dimension 1 we obtain a complete classification (i.e. a reduction to questions about associative division algebras). The main tools are representation theory of Lie algebras over algebraically closed and non-closed fields, and results about simple associative algebras in order to control the interplay between linear Lie algebras and the associative algebras generated by them. The relation to nearfields and left-symmetric division algebras is also discussed. |
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Keywords: | |
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