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CATEGORIES:The Archimedeans (CU Mathematical Society)
SUMMARY:Spin and Division Algebras - Dr Jonathan Evans (DA
MTP)
DTSTART;TZID=Europe/London:20120127T190000
DTEND;TZID=Europe/London:20120127T200000
UID:TALK36114AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/36114
DESCRIPTION:(Free for members\, £2 for non-members) \n\nThe co
ncept of a division algebra generalizes the real a
nd complex numbers by requiring a multiplication w
ith suitable properties to be defined on a normed
vector space. There are actually just two new poss
ibilities in higher dimensions\, known as the quat
ernions (dimension 4) and octonions (dimension 8).
Spin\, on the other hand\, refers to a particular
way of realizing rotational transformations in 3
or higher dimensions. The distinctive mathematical
properties which emerge are also of great importa
nce in physics\, since the description of many ele
mentary particles (quarks\, electrons\, neutrinos)
relies on spin representations. There are some fa
scinating inter-relationships between spin and div
ision algebras\, leading ultimately to concepts su
ch as triality\, supersymmetry and exceptional Lie
groups. My aim in this talk will be to give an ov
erview of some of these ideas.
LOCATION:Centre for Mathematical Sciences (CMS)
CONTACT:
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