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Classifying simple algebraic groups

**Skip Garibaldi**,

UCLA

Abstract: The classification of simple Lie algebras over the

reals and complexes has been known for a long time. But over

an arbitrary field, the question is quite a bit more complicated.

(For example, in characteristic $p$, one should probably look

at algebraic groups instead of Lie algebras.) The classification

is still very far from being resolved, and some conjectures due

to Serre and others are equivalent to special cases of it.