BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Justin McInroy (University of Chester\, UK) DTSTART:20230213T150000Z DTEND:20230213T160000Z DTSTAMP:20260423T021125Z UID:ENAAS/6 DESCRIPTION:Title: Cl assifying quotients of the Highwater algebra\nby Justin McInroy (Unive rsity of Chester\, UK) as part of European Non-Associative Algebra Seminar \n\n\nAbstract\nAxial algebras are a class of non-associative algebras wit h a strong natural link to groups and have recently received much attentio n. They are generated by axes which are semisimple idempotents whose eige nvectors multiply according to a so-called fusion law. Of primary interes t are the axial algebras with the Monster type $(\\alpha\, \\beta)$ fusion law\, of which the Griess algebra (with the Monster as its automorphism g roup) is an important motivating example.\n\nBy previous work of Yabe\, an d Franchi and Mainardis\, any symmetric 2-generated axial algebra of Monst er type $(\\alpha\, \\beta)$ is either in one of several explicitly known families\, or is a quotient of the infinite-dimensional Highwater algebra $\\mathcal{H}$\, or its characteristic 5 cover $\\hat{\\mathcal{H}}$. We complete this classification by explicitly describing the infinitely many ideals and thus quotients of the Highwater algebra (and its cover). As a consequence\, we find that there exist 2-generated algebras of Monster typ e $(\\alpha\, \\beta)$ with any number of axes (rather than just $1\, 2\, 3\, 4\, 5\, 6\, \\infty$ as we knew before) and of arbitrarily large finit e dimension.\n\n\nIn this talk\, we will begin with a reminder of axial al gebras which were introduced last week.\n\n\nThis is joint work with:\nCla ra Franchi\, Catholic University of the Sacred Heart\, Milan\nMario Mainar dis\, University of Udine\n LOCATION:https://researchseminars.org/talk/ENAAS/6/ END:VEVENT END:VCALENDAR