1. Wilhelm Karl Joseph Killing was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry.
11 Facts About Wilhelm Killing
1. 2.
Wilhelm Killing taught in gymnasia from 1868 to 1872.
3.
Wilhelm Killing became a professor at the seminary college Collegium Hosianum in Braunsberg.
4.
Wilhelm Killing took holy orders in order to take his teaching position.
5.
Wilhelm Killing became rector of the college and chair of the town council.
6.
In 1878 Wilhelm Killing wrote on space forms in terms of non-Euclidean geometry in Crelle's Journal, which he further developed in 1880 as well as in 1885.
7.
Wilhelm Killing is credited with formulating transformations mathematically equivalent to Lorentz transformations in n dimensions in 1885.
8.
Wilhelm Killing invented Lie algebras independently of Sophus Lie around 1880.
9.
From 1888 to 1890, Wilhelm Killing essentially classified the complex finite-dimensional simple Lie algebras, as a requisite step of classifying Lie groups, inventing the notions of a Cartan subalgebra and the Cartan matrix.
10.
Wilhelm Killing thus arrived at the conclusion that, basically, the only simple Lie algebras were those associated to the linear, orthogonal, and symplectic groups, apart from a small number of isolated exceptions.
11.
Wilhelm Killing discovered the exceptional Lie algebra g2 in 1887; his root system classification showed up all the exceptional cases, but concrete constructions came later.