92 citations · 100 across the 8 of their papers we have counts for
13 papers
Geometry of quantum systems: density states and entanglement
Janusz Grabowski, Marek Kuś, Giuseppe Marmo
Various problems concerning the geometry of the space $u^*(\cH)$ of Hermitian operators on a Hilbert space $\cH$ are addressed. In particular, we study the canonical Poisson and Ri…
On Lie induction and the exceptional series
Jan E. Grabowski
Lie bialgebras occur as the principal objects in the infinitesimalisation of the theory of quantum groups - the semi-classical theory. Their relationship with the quantum theory ha…
A triple construction for Lie bialgebras
Jan E. Grabowski
We introduce and study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfeld double. The triple is itself a quasitriangular Lie bialgebra. We prove s…
Isomorphisms of algebras of smooth functions revisited
Janusz Grabowski
It is proved that isomorphisms between algebras of smooth functions on Hausdorff smooth manifolds are implemented by diffeomorphisms. It is not required that manifolds are second c…
Lie algebraic characterization of manifolds
Janusz Grabowski, Norbert Poncin
Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particul…
Jacobi structures on affine bundles
J. Grabowski, D. Iglesias, J. C. Marrero +2
We study affine Jacobi structures on an affine bundle , i.e. Jacobi brackets that close on affine functions. We prove that there is a one-to-one correspondence between af…