132 citations · 1.9k across the 101 of their papers we have counts for
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Algebroids - general differential calculi on vector bundles
Janusz Grabowski, Pawel Urbanski
A notion of an algebroid - a generalization of a Lie algebroid structure is introduced. We show that many objects of the differential calculus on a manifold M associated with the c…
On Quantizing Nilpotent and Solvable Basic Algebras
Mark J. Gotay, Janusz Grabowski
We prove an algebraic ``no-go theorem'' to the effect that a nontrivial Poisson algebra cannot be realized as an associative algebra with the commutator bracket. Using this, we sho…
On Filippov algebroids and multiplicative Nambu-Poisson structures
Janusz Grabowski, Giuseppe Marmo
We discuss relations between linear Nambu-Poisson structures and Filippov algebras and define Filippov algebroids which are n-ary generalizations of Lie algebroids. We also prove r…
Remarks on Nambu-Poisson and Nambu-Jacobi brackets
Janusz Grabowski, Giuseppe Marmo
It is shown that Nambu-Poisson and Nambu-Jacobi brackets can be defined inductively: a n-bracket, n>2, is Nambu-Poisson (resp. Nambu-Jacobi) if and only if fixing an argument we ge…