BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.bham.ac.uk//v3//EN
BEGIN:VEVENT
CATEGORIES:Algebra Seminar
SUMMARY:The general Sakuma Theorem - Sergey Shpectorov\, U
niversity of Birmingham
DTSTART:20200227T160000Z
DTEND:20200227T170000Z
UID:TALK4177AT
URL:/talk/index/4177
DESCRIPTION:The original Sakuma Theorem classifies vertex oper
ator algebras (VOAs) generated by two Ising vector
s. The properties it relies on were turned by Ivan
ov into the axioms of a new class of non-associati
ve algebras called Majorana algebras and thus axia
l algebras were born. \n\nThe first axial version
of the Sakuma theorem (for Majorana algebras) was
published by Ivanov\, Pasechnik\, Seress and Shpec
torov in 2010 and it was followed in 2015 by a mor
e general version due to Hall\, Rehren and Shpecto
rov\, where many Majorana-specific assumptions wer
e removed. The same year\, Rehren attempted an eve
n more general version\, completely parting with M
ajorana restrictions and \nallowing arbitrary para
meters a and b in the fusion rules to substitute t
he Majorana-specific values a=1/4 and b=1/32. He d
id not manage to obtain a complete classification\
, but he did show that the dimension of a 2-genera
ted algebra is \nbounded by eight except when a=2b
or a=4b.\n\nIn a joint project with Franchi and M
ainardis\, we reprove and generalise Rehren's theo
rem to cover also the exceptional cases. In the ca
se a=2b\, we obtain the same bound\, 8\, on the di
mension of a 2-generated algebra\, although for a
different \nspanning set. Even more interesting is
the other exceptional case\, where a=4b. Here we
also have the upper bound eight\, except when a=2
and b=1/2. In this final case\, we found an unexpe
cted example of an infinite dimensional 2-generate
d \nalgebra.
LOCATION:Lecture Theatre B\, Watson Building
CONTACT:Simon Goodwin
END:VEVENT
END:VCALENDAR