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SUMMARY:Isotropy of Tits construction
DTSTART;VALUE=DATE-TIME:20211112T093000Z
DTEND;VALUE=DATE-TIME:20211112T095500Z
DTSTAMP;VALUE=DATE-TIME:20260819T201335Z
UID:indico-contribution-310@indico.eimi.ru
DESCRIPTION:Speakers: Victor Petrov (SPbU)\nTits construction produces a 
 Lie algebra out of a composition algebra and an exceptional Jordan algeb
 ra. The type of the result is $F_4$\, ${}^2E_6$\, $E_7$ or $E_8$ when th
 e composition algebra has dimension 1\,2\,4 or 8 respectively. Garibaldi a
 nd Petersson noted that the Tits index ${}^2E_6^{35}$ cannot occur as a 
 result of Tits construction. Recently Alex Henke proved that the Tits
  index $E_7^{66}$ is also not possible. We push the analogy further and s
 how that Lie algebras of Tits index $E_8^{133}$ don't lie in the image
  of the Tits construction. The proof relies on basic facts about symme
 tric spaces and our joint result with Garibaldi and Semenov about isotrop
 y of groups of type $E_7$ in terms of the Rost invariant. This is a 
 part of a work joint with Simon Rigby.\n\nhttps://indico.eimi.ru/event/
 437/contributions/310/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/310/
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