An algebra over a field consists of a “space” named for these objects that has a bilinear product. For 10 points each:
[10e] Name these objects have a magnitude and direction.
ANSWER: vectors [accept vector spaces]
[10m] This mathematician names a non-associative algebra that pairs a vector space with his namesake commutator bracket denoted “x y minus y x.” This mathematician names groups that are also differentiable manifolds.
ANSWER: Sophus Lie (“lee”) [or Marius Sophus Lie; accept Lie groups; accept Lie bracket; accept Lie algebra]
[10h] This adjective is prefixed by “semi” to describe Lie algebras that have a non-degenerate Killing form. Lie algebras described by this adjective are non-abelian (“non-uh-BEE-lee-un”) and contain no non-zero proper ideals.
ANSWER: simple [accept simple Lie algebras; accept semisimple Lie algebras]
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