In physics and in mathematics Z 2 n-gradings, n≥ 2, appear in various fields. The
corresponding sign rule is determined by the “scalar product” of the involved Z 2 n-degrees …

We define the notions of trace, determinant and, more generally, Berezinian of matrices over
a [Formula: see text]-graded commutative associative algebra A. The applications include a …

Smooth Z 2 n-supermanifolds have been introduced and studied recently. The
corresponding sign rule is given by the 'scalar product'of the involved Z 2 n-degrees. It …

We prove that the category of ℤ2 n-manifolds has all finite products. Further, we show that a
ℤ2 n-manifold (resp., a ℤ2 n-morphism) can be reconstructed from its algebra of global ℤ2 n …

Abstract In Physics and in Mathematics Zn 2-gradings, n≥ 2, do appear quite frequently.
The corresponding sign rules are determined by the 'scalar product'of the involved Zn 2 …

We consider the short-wave limit of evolutionary wave equations to derive the Hamilton–
Jacobi equation. In particular we consider how to get wave mechanics from the abstract …

We prove that a vector bundle π: E→ M is characterized by the Lie algebra generated by all
differential operators on E which are eigenvectors of the Lie derivative in the direction of the …

We report on Koszul-Tate resolutions in Algebra, in Mathematical Physics, in Cohomological
Analysis of PDE-s, and in Homotopy Theory. Further, we define an abstract Koszul-Tate …

Two revolutionary physical theories appeared at the beginning of the 20th century, general
relativity and quantum mechanics. Curved spacetime, introduced to deal with gravitation …

In Physics and in Mathematics $\mathbb {Z} _2^ n $-gradings, $ n\geq 2$, do appear quite
frequently. The corresponding sign rules are determined by thescalar product'of the involved …