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 …

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 …

Metric-affine and generalized geometries are arguably the appropriate mathematical
frameworks for Einstein's theory of gravity and lowenergy effective string field theory …

Drinfel'd double of Lie bialgebroids plays an important role in T-duality of string theories. In
the presence of $ H $ and $ R $ fluxes, Lie bialgebroids should be extended to proto Lie …

In this work we study discrete analogues of an exact sequence of vector bundles introduced
by M. Atiyah in 1957, associated to any smooth principal G-bundle π: Q→ Q/G. In the original …

Tulczyjew’s triplet with an Ehresmann connection I: Trivialization and reduction Page 1
International Journal of Geometric Methods in Modern Physics Vol. 20, No. 4 (2023) 2350059 (37 …

We extend the notion of a natural fibre bundle by requiring diffeomorphisms of the base to lift
to automorphisms of the bundle only infinitesimally, ie at the level of the Lie algebra of vector …

Darboux theorem in symplectic geometry is the crux of emergent gravity in which the
gravitational metric emerges from a noncommutative U (1)-theory. Topological T-duality, on …

Celem niniejszej rozprawy doktorskiej jest znalezienie formalizmu matematycznego
opisującego w sposób jasny i koncepcyjnie prosty klasyczne teorie pola z cechowaniem. W …