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BEGIN:VEVENT
DTSTAMP:20211105T113714Z
DTSTART:20211109T130000Z
DTEND:20211109T140000Z
SUMMARY:Manchester Algebra Seminar - Justin Mcinroy
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}loi-kv6ci5u
0-q68frn
DESCRIPTION:Speaker: Justin Mcinroy - Bristol\n\nTitle: Classifying quo
tients of the Highwater algebra\n\nAbstract:\nAxial algebras are a new c
lass of non-associative algebras which have a strong link to groups. The
y are generated by axes which are semisimple idempotents whose eigenvect
ors multiply according to a so-called fusion law. The prototypical examp
le is the Griess algebra whose automorphism group is the Monster. The ei
genvalues for the axes in the Griess algebra are 1\, 0\, 1/4 and 1/32 an
d we call the fusion law Monster type M(1/4\, 1/32).\n\nRecently Yabe ha
s classified all the symmetric 2-generated axial algebras with the gener
alised Monster fusion law $\\mathcal{M}(\\alpha\, \\beta)$\, where $\\al
pha$ and $\\beta$ are indeterminants. He showed they either belong to a
list of families of algebras\, or are a quotient of the infinite-dimensi
onal Highwater algebra\, or its characteristic 5 cover. We classify all
the ideals of the Highwater algebra (and its cover) and hence make Yabe
’s classification explicit. As a consequence\, we find that there exist
2-generated algebras of Monster type $\\mathcal{M}(\\alpha\, \\beta)$ wi
th any number of axes (rather than just $1\,2\,3\,4\,5\,6\, \\infty$ as
we knew before) and of arbitrarily large but finite dimension.\n\nIn thi
s talk\, we do not assume any knowledge of axial algebras.\n\nThis is jo
int work with:\nClara Franchi\, Catholic University of the Sacred Heart\
, Milan\nMario Mainardis\, University of Udine\n\nPlace: Frank Adams (an
d to be streamed online*)\n\n*subject to equipment and connection\n\nTea
and biscuits 12:45 in the foyer
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams\, Alan Turing Building\, Manchester
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