caa a22 4500 445836512 CHVBK 20180317145331.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00209-010-0763-9 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0763-9 Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras [Elektronische Daten] [Michael Bate, Benjamin Martin, Gerhard Röhrle, Rudolf Tange] Let H be a reductive subgroup of a reductive group G over an algebraically closed field k. We consider the action of H on G n , the n-fold Cartesian product of G with itself, by simultaneous conjugation. We give a purely algebraic characterization of the closed H-orbits in G n , generalizing work of Richardson which treats the case H = G. This characterization turns out to be a natural generalization of Serre's notion of G-complete reducibility. This concept appears to be new, even in characteristic zero. We discuss how to extend some key results on G-complete reducibility in this framework. We also consider some rationality questions. Springer-Verlag, 2010 Conjugacy classes of n -tuples nationallicence G -complete reducibility nationallicence Bate Michael Department of Mathematics, University of York, YO10 5DD, York, UK aut Martin Benjamin Mathematics and Statistics Department, University of Canterbury, Private Bag 4800, Christchurch 1, New Zealand aut Röhrle Gerhard Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum, Germany aut Tange Rudolf Department of Mathematics, University of York, YO10 5DD, York, UK aut Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 809-832 0025-5874 269:3-4<809 2011 269 209 https://doi.org/10.1007/s00209-010-0763-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0763-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bate Michael Department of Mathematics, University of York, YO10 5DD, York, UK aut NATIONALLICENCE 700 1- Martin Benjamin Mathematics and Statistics Department, University of Canterbury, Private Bag 4800, Christchurch 1, New Zealand aut NATIONALLICENCE 700 1- Röhrle Gerhard Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum, Germany aut NATIONALLICENCE 700 1- Tange Rudolf Department of Mathematics, University of York, YO10 5DD, York, UK aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 809-832 0025-5874 269:3-4<809 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer