Supersymmetric Model with Grassmann-odd Lagrangian

A supersymmetric $D = 1, N =1$ model with a Grassmann-odd Lagrangian is proposed which, in contrast to the model with an even Lagrangian, contains not only a kinetic term but also an interaction term for the coordinates entering into one real scalar Grassmann-even (bosonic) superfield.Comment: 6 pages, LATEX 2e. The talk given at the International Conference "Supersymmetries and Quantum Field Theory" (SSQFT'2000, NSC KIPT, Kharkov, Ukraine, 25-29 July, 2000). To be published in the Proceedings of this Conference. Corrections of misprint

Gauge semi-simple extension of the Poincar\'e group

Based on the gauge semi-simple tensor extension of the Poincar\'e group another alternative approach to the cosmological term problem is proposed.Comment: Latex, 4 pages. 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

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