Packet E: Bonus 2
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]
<Toronto B, Other Science> | Packet E - Chicago A, Toronto B, Brandeis B, JHU A
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 73 | 14.93 | 99% | 40% | 11% |
Conversion
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| California (North) | Main Site | ✓ | 3 | 26.67 | 100% | 100% | 67% |
| California (South) | Main Site | ✓ | 4 | 17.50 | 100% | 75% | 0% |
| Canada | Main Site | ✓ | 1 | 20.00 | 100% | 100% | 0% |
| Florida | Main Site | ✓ | 3 | 13.33 | 100% | 33% | 0% |
| Great Lakes | Main Site | ✓ | 5 | 14.00 | 100% | 40% | 0% |
| Lower Mid-Atlantic | Main Site | ✓ | 8 | 12.50 | 100% | 25% | 0% |
| Midwest | Main Site | ✓ | 8 | 15.00 | 100% | 38% | 13% |
| Northeast | Main Site | ✓ | 5 | 16.00 | 100% | 40% | 20% |
| Overflow | Main Site | ✓ | 3 | 10.00 | 100% | 0% | 0% |
| South Central | Main Site | ✓ | 2 | 10.00 | 100% | 0% | 0% |
| Southeast | Main Site | ✓ | 7 | 14.29 | 100% | 29% | 14% |
| UK | Main Site | ✓ | 12 | 15.83 | 92% | 50% | 17% |
| Upper Mid-Atlantic | Main Site | ✓ | 8 | 13.75 | 100% | 38% | 0% |
| Upstate NY | Main Site | ✓ | 4 | 15.00 | 100% | 25% | 25% |