132 citations · 1.9k across the 101 of their papers we have counts for
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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…
Homology and modular classes of Lie algebroids
Janusz Grabowski, Giuseppe Marmo, Peter W. Michor
For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid…
Quasi-derivations and QD-algebroids
Janusz Grabowski
Axioms of Lie algebroid are discussed in order to review some known aspects for non-experts. In particular, it is shown that a Lie QD-algebroid (i.e. a Lie algebra bracket on the F…