A. L. Onishchik

A Spectral Sequence for the Tangent Sheaf Cohomology of a Supermanifold

We construct a spectral sequence permitting to compute the tangent sheaf cohomology of a complex analytic supermanifold in terms of the tangent sheaf cohomology of the associated split supermanifold. The first coboundary operators of this sequence are determined, and the example of the superquadric in the projective superplane is studied.

Semidirect sums of Lie algebras

AbstractThis paper examines the problem of classifying finite-dimensional Lie algebras over the field C with a given radical

Completely integrable equations on homogeneous spaces

\mathfrak{r}

Pseudoconvexity in the theory of complex spaces

and also the problem of classifying algebraic Lie algebras with a given nilpotent radical

Compact Homogeneous Spaces

\mathfrak{r}

Real Semisimple Lie Groups

. A detailed study is made of the case when