132 citations · 1.9k across the 101 of their papers we have counts for
31 papers · 1 filter
Symplectic -manifolds
Andrew James Bruce, Janusz Grabowski
Roughly speaking, -manifolds are `manifolds' equipped with -graded commutative coordinates with the sign rule being determined by the scalar product…
Discrete mechanics on unitary octonions
Janusz Grabowski, Zohreh Ravanpak
In this article we generalize the discrete Lagrangian and Hamiltonian mechanics on Lie groups to non-associative objects generalizing Lie groups (smooth loops). This shows that the…
Riemannian structures on -manifolds
Andrew James Bruce, Janusz Grabowski
Very loosely, -manifolds are `manifolds' with -graded coordinates and their sign rule is determined by the scalar product of their -…
Odd Connections on Supermanifolds: Existence and relation with Affine Connections
Andrew James Bruce, Janusz Grabowski
The notion of an odd quasi-connection on a supermanifold, which is loosely an affine connection that carries non-zero Grassmann parity, is examined. Their torsion and curvature are…
Lie groupoids in information geometry
Katarzyna Grabowska, Janusz Grabowski, Marek Kuś +1
We demonstrate that the proper general setting for contrast (potential) functions in statistical and information geometry is the one provided by Lie groupoids and Lie algebroids. T…
Remarks on superdifferential equations
Janusz Grabowski, Javier de Lucas
We show that the term `superdifferential equation' has been employed in the literature to refer to different types of differential equations with even and odd variables. It is just…