BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ignacio Bajo (University of Vigo\, Spain) DTSTART:20240923T150000Z DTEND:20240923T160000Z DTSTAMP:20260423T035616Z UID:ENAAS/101 DESCRIPTION:Title: Quadratic Lie algebras admitting 2-plectic structures\nby Ignacio Bajo (University of Vigo\, Spain) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nA 2-plectic form ω on a Lie algebra is a 3-form on the algebra such that it is closed and non-degenerate in the sense that\, for every nonzero x\, the bilinear form ω(x\, ·\, ·) is not identicall y zero. We will study the existence of 2-plectic structures on the so-call ed quadratic Lie algebras\, which are Lie algebras admitting an ad-invaria nt pseudo-Euclidean product. It is well-known that every centerless quadra tic Lie algebra admits a 2-plectic form but not many quadratic examples wi th nontrivial center are known. We give several constructions to obtain la rge families of 2-plectic quadratic Lie algebras with nontrivial center\, many of them among the class of nilpotent Lie algebras. We give some suffi cient conditions to assure that certain extensions of 2-plectic quadratic Lie algebras result to be 2-plectic as well. For instance\, we show that o scillator algebras can be naturally endowed with 2-plectic structures. We prove that every quadratic and symplectic Lie algebra with dimension great er than 4 also admits a 2-plectic form. Further\, conditions to assure tha t one may find a 2-plectic which is exact on certain quadratic Lie algebra s are obtained.\n LOCATION:https://researchseminars.org/talk/ENAAS/101/ END:VEVENT END:VCALENDAR