arXiv subjects
Publications and source records attributed to P. W. Michor.
Pulling back sets of functions in involution by Poisson mappings and adding Casimir functions during the process allows to construct completely integrable systems. Some examples are investigated in detail.
Lie bialgebra structures are reviewed and investigated in terms of the double Lie algebra, of Manin- and Gauß-decompositions. The standard R-matrix in a Manin decomposition then gives rise to several Poisson structures on the correponding double group, which is investigated in great detail.
There is a canonical mapping from the space of sections of the bundle $\wedge T^\ast M\otimes ST\ M$ to $Ω(T^\ast M ; T(T^\ast M))$. It is shown that this is a homomorphism on $Ω(M;TM) for the Frölicher-Nijenhuis brackets, and also on $Γ(ST\ M)$ for the Schouten bracket of symmetric multi vector fields. But the whole image is not a subalgebra for the Frölicher-Nijenhuis bracket on $Ω(T^\ast M;T(T^\ast M))$.