Transformations of Grassmannians and automorphisms of linear groups

Abstract

We consider transformations preserving certain linear structure in Grassmannians and give some generalization of the Fundamental Theorem of Projective Geometry and the Chow Theorem [Ch]. It will be exploited to study linear $(k,n-k)$-involutions, $1<k<n-1$. The analogy of the well-known J. Dieudonn\'{e} and C. E. Rickart result will be obtained.