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SUMMARY:Karel Dekimpe (Catholic University of Leuven\, Belgium)
DTSTART:20230123T150000Z
DTEND:20230123T160000Z
DTSTAMP:20260423T052456Z
UID:ENAAS/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/3/">Di
 -semisimple Lie algebras and applications in post-Lie algebra structures</
 a>\nby Karel Dekimpe (Catholic University of Leuven\, Belgium) as part of 
 European Non-Associative Algebra Seminar\n\n\nAbstract\nWe call a Lie alge
 bra $\\mathfrak g$ di-semisimple if it can be written as a vector space su
 m $\\mathfrak g = \\mathfrak s_1 + \\mathfrak s_2$\, where $\\mathfrak s_1
 $ and $\\mathfrak s_2$ are semisimple subalgebras of $\\mathfrak g$ and we
  say that $\\mathfrak g$ is strongly di-semisimple  if $\\mathfrak g$ can 
 be written as a direct vector space sum of semisimple subalgebras. We will
  show that complex strongly di-semisimple Lie algebras have to be semisimp
 le themselves. \n\nWe will then use this result to show that if a pair of 
 complex Lie algebras $(\\mathfrak g\, \\mathfrak n)$ with $\\mathfrak g$ s
 emisimple admits a so called post-Lie algebra structure\, then \n$\\mathfr
 ak n$ must be isomorphic to $\\mathfrak g$. \n\nJoint work with Dietrich B
 urde and Mina Monadjem.\n
LOCATION:https://researchseminars.org/talk/ENAAS/3/
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