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SUMMARY:Adela Latorre (Polytechnic University of Madrid\, Spain)
DTSTART:20230313T150000Z
DTEND:20230313T160000Z
DTSTAMP:20260423T052459Z
UID:ENAAS/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/10/">S
 olvable Lie algebras with complex symplectic structures</a>\nby Adela Lato
 rre (Polytechnic University of Madrid\, Spain) as part of European Non-Ass
 ociative Algebra Seminar\n\n\nAbstract\nLet $\\mathfrak g$ be a $2n$-dimen
 sional solvable Lie algebra. A complex structure on $\\mathfrak g$ is an e
 ndomorphism $J$ that satisfies $J^2=-Id$ and $N_J(X\,Y)=0$\, for every $X\
 ,Y\\in\\mathfrak g$\, being\n$$N_J(X\,Y):=[X\,Y]+J[JX\,Y]+J[X\,JY]-[JX\,JY
 ].$$ \nSuppose that $\\mathfrak g$ simultaneously admits a complex structu
 re $J$ and a symplectic structure $\\omega$ (i.e.\, a closed $2$-form $\\o
 mega\\in\\wedge^2\\mathfrak g^*$ such that $\\omega^n\\neq 0$). \nAlthough
  $J$ and $\\omega$ are initially two unrelated structures\, one can ask fo
 r an additional condition involving both of them.\nIn this sense\, the pai
 r $(J\,\\omega)$ is said to be a complex symplectic structure if $J$ is sy
 mmetric with respect to $\\omega$\, in the sense that $\\omega(JX\,Y)=\\om
 ega(X\,JY)$\, for every $X\,Y\\in\\mathfrak g$.\nIn this talk\, we will pr
 esent some methods to find certain types of solvable Lie algebras (such as
  nilpotent or almost Abelian) admitting complex symplectic structures.\n
LOCATION:https://researchseminars.org/talk/ENAAS/10/
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