Exterior Differentials in Superspace and Poisson Brackets of Diverse Grassmann Parities

It is shown that two definitions for the exterior differential in superspace, giving the same exterior calculus, when applied to the Poisson bracket lead to the different results. Examples of the even and odd linear brackets, corresponding to semi-simple Lie groups, are given and their natural connection with BRST and anti-BRST charges is indicated.Comment: 5 pages, LATEX 2.09. The talk at the 9th International Conference on Supersymmetry and Unification of Fundamental Interactions (SUSY'01, JINR, Dubna, Russia, 11-17 June, 2001). To be published in the Proceedings of this Conference. Correction of misprint

Semi-simple extension of the (super)Poincar\'e algebra

A semi-simple tensor extension of the Poincar\'e algebra is proposed for the arbitrary dimensions $D$. A supersymmetric also semi-simple generalization of this extension is constructed in the D=4 dimensions. This paper is dedicated to the memory of Anna Yakovlevna Gelyukh.Comment: LaTeX, 9 pages. Some specifications are adde

Multiplet with components of different masses

A principle possibility for the existence of a multiplet including the components with the different masses is indicated. This paper is dedicated to the memory of Anna Yakovlevna Gelyukh (Kalaida).Comment: Latex, 6 pages. Two specifications are added in the section "Multiplet". Correction of misprints. The title is changed and a reference is adde