Integrals of functions on an object named for this mathematician can be computed via integrals over a maximal torus by Weyl's integral formula. Root systems of objects named for this mathematician are classified in Dynkin diagrams. Objects named for this (15[1])mathematician are semisimple if and only if their associated Killing form is non-degenerate, according to Cartan’s criterion. The tangent space at the identity of an object named for this mathematician is isomorphic to the space of (*) left-invariant vector fields on said object. Another object named for this mathematician is a vector space together with a bilinear map that is antisymmetric, satisfies the Jacobi identity, and is denoted by a pair of square brackets. For 10 points, groups that are also differentiable manifolds are named for what Norwegian mathematician? (-5[1])■END■ (10[1]0[1])