Moore-Penrose inverse, parabolic subgroups, and Jordan pairs

Details Moore-Penrose inverse, parabolic subgroups, and Jordan pairs Moore-Penrose inverse, parabolic subgroups, and Jordan pairs

2001-01-12

arxiv.org/abs/math/0101107v1

Mathematics

Representation Theory

18 pages

Scientific paper

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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