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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Classifying quotients of the Highwater algebra - J
ustin McInroy (University of Chester)
DTSTART;TZID=Europe/London:20220727T100000
DTEND;TZID=Europe/London:20220727T103000
UID:TALK176555AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/176555
DESCRIPTION:Axial algebras are a class of non-associative alge
bras with a strong natural link to groups and have
recently received much attention. \; They are
generated by axes which are semisimple idempotent
s whose eigenvectors multiply according to a so-ca
lled fusion law. \; Of primary interest are th
e axial algebras with the Monster type $(\\alpha\,
\\beta)$ fusion law\, of which the Griess algebra
(with the Monster as its automorphism group) is a
n important motivating example.\nBy previous work
of Yabe\, and Franchi and Mainardis\, any symmetri
c 2-generated axial algebra of Monster type $(\\al
pha\, \\beta)$ is either in one of several explici
tly known families\, or is a quotient of the infin
ite-dimensional Highwater algebra $\\mathcal{H}$\,
or its characteristic 5 cover $\\hat{\\mathcal{H}
}$. \; We complete this classification by expl
icitly describing the infinitely many ideals and t
hus quotients of the Highwater algebra (and its co
ver). \; As a consequence\, we find that there
exist 2-generated algebras of Monster type $\\mat
hcal{M}(\\alpha\, \\beta)$ with any number of axes
(rather than just $1\,2\,3\,4\,5\,6\, \\infty$ as
we knew before) and of arbitrarily large finite d
imension.\nIn this talk\, we do not assume any kno
wledge of axial algebras.\nThis is joint work with
:Clara Franchi\, Catholic University of the Sacred
Heart\, MilanMario Mainardis\, University of Udin
e
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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