11 citations · 31 across the 9 of their papers we have counts for
9 papers
Cyclic Lie-Rinehart algebras
Daniel Beltita, Alina Dobrogowska, Grzegorz Jakimowicz
We study Lie-Rinehart algebra structures in the framework provided by a duality pairing of modules over a unital commutative associative algebra. Thus, we construct examples of Lie…
A new look at Lie algebras
Alina Dobrogowska, Grzegorz Jakimowicz
We present a new look at description of real finite-dimensional Lie algebras. The basic element turns out to be a pair consisting of a linear mapping and its…
Complete and vertical lifts of Poisson vector fields and infinitesimal deformations of Poisson tensor
Alina Dobrogowska, Grzegorz Jakimowicz, Karolina Wojciechowicz
In this paper we prove that both complete and vertical lifts of a Poisson vector field from a Poisson manifold to its tangent bundle are also Poisson. We us…
Deformation of algebroid bracket of differential forms and Poisson manifold
Alina Dobrogowska, Grzegorz Jakimowicz, Karolina Wojciechowicz
We construct the family of algebroid brackets on the tangent bundle to a Poisson manifold starting from an algebroid bracket of differential fo…
Banach-Lie groupoids and generalized inversion
Daniel Beltiţă, Tomasz Goliński, Grzegorz Jakimowicz +1
We study a few basic properties of Banach-Lie groupoids and algebroids, adapting some classical results on finite dimensional Lie groupoids. As an illustration of the general theor…
Symmetries of the space of connections on a principal G-bundle and related symplectic structures
Grzegorz Jakimowicz, Anatol Odzijewicz, Aneta Sliżewska
We investigate G-invariant symplectic structures on the cotangent bundle T*P of a principal G-bundle P(M,G) which are canonically related to automorphisms of the tangent bundle TP…