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SUMMARY:Seidon Alsaody (Uppsala University\, Sweden)
DTSTART:20230116T150000Z
DTEND:20230116T160000Z
DTSTAMP:20260423T035409Z
UID:ENAAS/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/2/">Br
 own algebras\, Freudenthal triple systems and exceptional groups over ring
 s</a>\nby Seidon Alsaody (Uppsala University\, Sweden) as part of European
  Non-Associative Algebra Seminar\n\n\nAbstract\nExceptional algebraic grou
 ps are intimately related to various classes of non-associative algebras: 
 for example\, octonion algebras are related to groups of type $G_2$ and $D
 _4$\, and Albert algebras to groups of type $F_4$ and $E_6$. This can be u
 sed\, on the one hand\, to give concrete descriptions of homogeneous space
 s under these groups and\, on the other hand\, to parametrize isotopes of 
 these algebras using said homogeneous spaces. The key tools are provided b
 y the machinery of torsors and faithfully flat descent\, working over arbi
 trary commutative rings (sometimes assuming 2 and 3 to be invertible).\n\n
 I will talk about recent work where we do this from Brown algebras and the
 ir associated Freudenthal triple systems\, whose automorphism groups are o
 f type $E_6$ and $E_7$\, respectively. I will hopefully be able to show ho
 w algebraic and geometric properties come together in this picture.\n
LOCATION:https://researchseminars.org/talk/ENAAS/2/
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