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SUMMARY:Spin and Division Algebras - Dr Jonathan Evans (DAMTP)
DTSTART:20120127T190000Z
DTEND:20120127T200000Z
UID:TALK36114@talks.cam.ac.uk
CONTACT:25292
DESCRIPTION:(Free for members\, £2 for non-members) \n\nThe concept of a 
 division algebra generalizes the real and complex numbers by requiring a m
 ultiplication with suitable properties to be defined on a normed vector sp
 ace. There are actually just two new possibilities in higher dimensions\, 
 known as the quaternions (dimension 4) and octonions (dimension 8). Spin\,
  on the other hand\, refers to a particular way of realizing rotational tr
 ansformations in 3 or higher dimensions. The distinctive mathematical prop
 erties which emerge are also of great importance in physics\, since the de
 scription of many elementary particles (quarks\, electrons\, neutrinos) re
 lies on spin representations. There are some fascinating inter-relationshi
 ps between spin and division algebras\, leading ultimately to concepts suc
 h as triality\, supersymmetry and exceptional Lie groups. My aim in this t
 alk will be to give an overview of some of these ideas.
LOCATION:Centre for Mathematical Sciences (CMS)
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