Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • 5 - Complete reducibility and subgroups of exceptional algebraic groups

  • Edited by C. M. Campbell, University of St Andrews, Scotland, M. R. Quick, University of St Andrews, Scotland, E. F. Robertson, University of St Andrews, Scotland, C. M. Roney-Dougal, University of St Andrews, Scotland, D. I. Stewart, University of Manchester
  • Book:
    Groups St Andrews 2022 in Newcastle
    Published online:
    21 November 2024
    Print publication:
    12 December 2024, pp 191-245

  • Summary

    This survey article has two components. The first part gives a gentle introduction to Serres notion of $G$-complete reducibility, where $G$ is a connected reductive algebraic group defined over an algebraically closed field. The second part concerns consequences of this theory when $G$ is simple of exceptional type, specifically its role in elucidating the subgroup structure of $G$. The latter subject has a history going back about sixty years. We give an overview of what is known, up to the present day. We also take the opportunity to offer several corrections to the literature.

  • Kneser–Tits for a rank 1 form of $E_6$ (after Veldkamp)

  • Skip Garibaldi
  • Journal:
    Compositio Mathematica / Volume 143 / Issue 1 / January 2007
    Published online by Cambridge University Press:
    19 January 2007, pp. 191-200
    Print publication:
    January 2007
    • Article
      • You have access
    • PDF
    • Export citation

  • We prove the Kneser-Tits conjecture for groups of index $^2E^{29}_{6,1}$ using an argument inspired by a 1968 paper by Veldkamp. We also prove that these groups are stably rational varieties.