Wilhelm Killing

From Biocrawler, the free encyclopedia.

Wilhelm Karl Joseph Killing (1847 May 10 – 1923 February 11) was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry.

Killing invented Lie algebras independently of Sophus Lie around 1880. He made important contributions to the classification of simple Lie algebras, inventing the notions of a Cartan subalgebra and the Cartan matrix. He also introduced the notion of a root system. He is the discoverer of the exceptional Lie algebra g₂ (in 1887); his root system classification showed up all the exceptional cases, but concrete constructions came later.

Killing also introduced the term characteristic equation of a matrix.

See also

• Killing form
• Killing vector field

External links

• Biography (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Killing.html) at the MacTutor archive

Wikipedia (http://en.wikipedia.org/wiki/Main_Page) Wilhelm_Killing (http://en.wikipedia.org/wiki/Wilhelm_Killing) version history (http://en.wikipedia.org/w/index.php?title=Wilhelm_Killing&action=history) GNU Free Documentation Lizenz (http://en.wikipedia.org/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License) CC-by-sa (http://creativecommons.org/licenses/by-sa/2.5/)

---