We extend certain homomorphisms defined on the higher Torelli subgroups of the mapping class group to crossed homomorphisms defined on the entire mapping class group. In particular, for every k ≥ 2, we construct a crossed homomorphism ǫk which extends Morita’s homomorphism τ̃k to the entire mapping class group. From this crossed homomorphism we also obtain a crossed homomorphism extending the kt...

We combine recent developments on weakly symmetric pseudo--riemannian nilmanifolds with geometric methods for construction of unitary representations square integrable Dolbeault cohomology spaces. This runs parallel to discrete series spaces harmonic forms values in holomorphic vector bundles over flag domains. Some special cases had been described by Satake 1971 and the author 1975. Here we de...

In our preceding paper we have introduced the notion of an s-homogeneous triple. this use technique to study connected algebras with two relations. For such algebras, describe all possible pairs (A,M), where A is s-Veronese ring and M (s,1)-Veronese bimodule dual algebra. each a pair classify corresponding or give necessary sufficient conditions for algebra under consideration correspond given ...