
Journal of Lie Theory 12 (2002), No. 2, 461481 Copyright Heldermann Verlag 2002 MoorePenrose Inverse, Parabolic Subgroups, and Jordan Pairs Evgueni Tevelev Moscow Independent University, B. Vlas'evsky 11, 121002 Moscow, Russia A MoorePenrose inverse of an arbitrary complex matrix A is defined as a unique matrix A^{+} such that AA^{+}A = A, A^{+}AA^{+} = A^{+}, and AA^{+}, A^{+}A are Hermite matrices. We show that this definition has a natural generalization in the context of shortly graded simple Lie algebras corresponding to parabolic subgroups with "aura" (abelian unipotent radical) in simple complex Lie groups, or equivalently in the context of simple complex Jordan pairs. We give further generalizations and applications. [ Fulltextpdf (283 KB)] 