BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Cristina Draper Fontanals (University of Málaga\, Spain) DTSTART:20251215T150000Z DTEND:20251215T160000Z DTSTAMP:20260423T035609Z UID:ENAAS/154 DESCRIPTION:Title: Revisiting simple Lie algebras from the view of the grading group\nby Cristina Draper Fontanals (University of Málaga\, Spain) as part of Europ ean Non-Associative Algebra Seminar\n\n\nAbstract\nIn this talk we discuss the role of gradings on Lie algebras and how they can be used to obtain s uitable models for a wide range of structures\, including simple\, solvabl e\, and nilpotent Lie algebras. We introduce the notion of a \\emph{genera lized group algebra}\, which provides a flexible framework for describing graded algebras in full generality. Although this concept may at first app ear too broad to be useful in the specific context of Lie algebras\, we sh all show how naturally it applies by examining several illustrative exampl es.\n\nA central theme will be the use of the \\emph{grading group} to gai n insight into structural properties of the underlying Lie algebra. For in stance\, viewing $\\mathfrak{so}(8)$ as a generalized group algebra sheds light on its spin representations and on the phenomenon of triality. More broadly\, this perspective greatly simplifies the construction of orthonor mal bases\, as in the case of $\\mathfrak{g}_2$.\n\nFinally\, we show that this approach renders the computation of brackets in Lie algebras obtaine d via \\emph{graded contractions} essentially immediate. This leads to vas t families of high-dimensional nonsimple Lie algebras with distinctive str uctural features\, obtained from the exceptional simple Lie algebras throu gh the Tits construction.\n LOCATION:https://researchseminars.org/talk/ENAAS/154/ END:VEVENT END:VCALENDAR