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Journal of Lie Theory 12 (2002), No. 2, 461--481
Copyright Heldermann Verlag 2002

Moore-Penrose Inverse, Parabolic Subgroups, and Jordan Pairs

Evgueni Tevelev
Moscow Independent University, B. Vlas'evsky 11, 121002 Moscow, Russia

A Moore-Penrose 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.

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