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On algebraic groups defined by Jordan pairs

Published online by Cambridge University Press:  22 January 2016

Ottmar Loos
Ottmar Loos*
Affiliation:
Department of Mathematics, University of British Columbia
*
Current address: Institut für Mathematik Universität InnsbruckInnsbruck, Austria
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Let G be an algebraic group over a field k, and let ψ be an action of the multiplicative group km of k on G by automorphisms. We say ψ is an elementary action if it has only the weights 0, ±1; more precisely, if there exist subgroups H, U+, U- of G such that (i) H is fixed under ψ, (ii) U+ and U+ are vector groups and (iii) Ω = U+. H . U+ is open in G, and (iv) G is generated by H, U+, U+. This situation is characteristic for the complexifications of the automorphism groups of bounded symmetric domains (see, e.g., [9, 16]). A typical example is G = GLnwith (matrices being decomposed into 4 blocks) ψ given by

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 74 , July 1979 , pp. 23 - 66
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

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