BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mikhail Kotchetov (Memorial University\, Canada) DTSTART:20250421T150000Z DTEND:20250421T160000Z DTSTAMP:20260423T035633Z UID:ENAAS/120 DESCRIPTION:Title: Almost fine gradings on algebras and classification of gradings up to isom orphism\nby Mikhail Kotchetov (Memorial University\, Canada) as part o f European Non-Associative Algebra Seminar\n\n\nAbstract\nSince the works of Patera-Zassenhaus (1989) and Bahturin-Sehgal-Zaicev (2001)\, the proble m of classifying gradings by groups on various algebras has received much attention. There are typically two kinds of classification of gradings on a given algebra A: fine gradings up to equivalence or all G-gradings\, for a fixed group G\, up to isomorphism. These classifications are related\, but it is not straightforward to pass from one to the other. In this talk\ , based on a recent paper with A. Elduque\, we introduce a class of gradin gs\, which we call almost fine\, on a finite-dimensional algebra A over an algebraically closed field\, such that every G-grading on A is obtained f rom an almost fine grading in an essentially unique way (which is not the case with fine gradings). For abelian groups\, we give a method of obtaini ng all almost fine gradings if fine gradings are known. If time permits\, we will illustrate this approach in the case of simple Lie algebras in cha racteristic 0: to any abelian group grading with nonzero identity componen t\, we attach a (possibly nonreduced) root system Φ and construct an adap ted Φ-grading.\n LOCATION:https://researchseminars.org/talk/ENAAS/120/ END:VEVENT END:VCALENDAR