Cohomology of real Lie algebras

Silhan Josef


We show how to describe the cohomology of a nilpotent part of some
parabolic subalgebra of a semisimple Lie algebra with values
in its irreducible representation. The situation
in the complex case is well--known, the Kostant's result (see below) gives
an explicit description of a representation of a proper reductive subalgebra
on the space of the complex cohomology. The aim of this work is to read the
structure of the real cohomology from the structure of the complex one.
We will use the notation of Dynkin and Satake diagrams for the description
of semisimple and parabolic real and complex Lie algebras and their

Lie algebra cohomology, parabolic subalgebra, real form, real cohomology

Math Review Classification

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