Strongly r-matrix induced tensors, Koszul cohomology, and arbitrary-dimensional quadratic Poisson cohomology

Mathematics – Symplectic Geometry

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

25 pages

Scientific paper

We introduce the concept of strongly $r$-matrix induced ({\small SRMI}) Poisson structure, report on the relation of this property with the stabilizer dimension of the considered quadratic Poisson tensor, and classify the Poisson structures of the Dufour-Haraki classification (DHC) according to their membership of the family of {\small SRMI} tensors. One of the main results of our work is a generic cohomological procedure for {\small SRMI} Poisson structures in arbitrary dimension. This approach allows decomposing Poisson cohomology into, basically, a Koszul cohomology and a relative cohomology. Moreover, we investigate this associated Koszul cohomology, highlight its tight connections with Spectral Theory, and reduce the computation of this main building block of Poisson cohomology to a problem of linear algebra. We apply these upshots to two structures of the DHC and provide an exhaustive description of their cohomology. We thus complete our list of data obtained in previous works, see \cite{MP} and \cite{AMPN}, and gain fairly good insight into the structure of Poisson cohomology.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Strongly r-matrix induced tensors, Koszul cohomology, and arbitrary-dimensional quadratic Poisson cohomology does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Strongly r-matrix induced tensors, Koszul cohomology, and arbitrary-dimensional quadratic Poisson cohomology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Strongly r-matrix induced tensors, Koszul cohomology, and arbitrary-dimensional quadratic Poisson cohomology will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-366816

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.