BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Louis Rowen (Bar-Ilan University\, Israel) DTSTART:20240506T150000Z DTEND:20240506T160000Z DTSTAMP:20260423T021125Z UID:ENAAS/68 DESCRIPTION:Title: W eakly primitive axial algebras\nby Louis Rowen (Bar-Ilan University\, Israel) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\ nIn earlier work we studied the structure of primitive axial algebras of Jordan type (PAJ's)\, not necessarily commutative\, in terms of their prim itive axes. In this paper we weaken primitivity and permit several pairs o f (left and right) eigenvalues satisfying a more general fusion rule\, bri nging in interesting new examples such as the band semigroup algebras and various noncommutative examples. Also we broaden our investigation to the case of 2-generated algebras for which only one axis satisfies the fusion rules. As an example we describe precisely the 2-dimensional axial algebra s and the 3-dimensional and 4-dimensional weakly primitive axial algebra s of Jordan type (weak PAJ's)\, and we see\, in contrast to the case for~P AJ's\, that there are higher dimensional weak PAJ's generated by two axes. We also prove a theorem that enables us to reduce weak PAJ's to uniform c omponents.\n LOCATION:https://researchseminars.org/talk/ENAAS/68/ END:VEVENT END:VCALENDAR