Hamilton described a generalization of the complex numbers named for the fact that every number could be obtained as a linear combination of this many ‘units’. For 10 points each:
[10e] The quaternions form a division algebra of what dimension over the reals?
ANSWER: four
[10m] The quaternions of unit magnitude are isomorphic to this Lie (“lee”) group used to describe spins as it forms the universal cover of the three dimensional rotation group.This is the group of 2 by 2 matrices with determinant one and equal to their adjoint.
ANSWER: SU(2) [or “special unitary group of order two”, prompt on SU by asking ‘which special unitary group?’]
[10h] Viewing the 3-sphere as a subset of the quaternions gives an easy construction of a fibre bundle named for this man whose fibres are circles and base space is the 2-sphere. This man also names the simplest link, made of two linked circles.
ANSWER: Heinz Hopf