Essential Variational Poisson Cohomology
Name
Kac_Essential variational.pdf
Size
328.74 KB
Format
Adobe PDF
Checksum (MD5)
4b836b8d6d3f51ce18f08a0ebf21a624
Author(s)
De Sole, Alberto
Kac, Victor
Date Issued
April 2012
Journal
Communications in Mathematical Physics
Publisher
Springer-Verlag
Citation
De Sole, Alberto, and Victor G. Kac. “Essential Variational Poisson Cohomology.” Commun. Math. Phys. 313, no. 3 (April 3, 2012): 837–864.
Version
Original manuscript
Abstract
In our recent paper “The variational Poisson cohomology” (2011) we computed the dimension of the variational Poisson cohomology H[subscript K](V) for any quasiconstant coefficient ℓ × ℓ matrix differential operator K of order N with invertible leading coefficient, provided that V is a normal algebra of differential functions over a linearly closed differential field. In the present paper we show that, for K skewadjoint, the Z -graded Lie superalgebra H[subscript K](V) is isomorphic to the finite dimensional Lie superalgebra [˜ over H](Nℓ,S) . We also prove that the subalgebra of “essential” variational Poisson cohomology, consisting of classes vanishing on the Casimirs of K, is zero. This vanishing result has applications to the theory of bi-Hamiltonian structures and their deformations. At the end of the paper we consider also the translation invariant case.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00220-012-1461-8
