Anatolij Prykarpatski
Affine Courant algebroid, its coadjoint orbits and related integrable systems
The Poisson structures related with the affine Courant algebroid are analyzed. The coadjoint action orbits are studied, infinite hierarchies of the Casimir functionals are described. A wide class of integrable flows on functional manifolds is considered.
The Lie algebroid as a mathematical object is an unrecognized part of the folklore of differential geometry. They have been introduced repeatedly [3,5] into differential geometry since the early 1950's, and also into physics and algebra, under a wide variety of names, chiefly as infinitesimal invariants associated to geometric structures: in connection theory, as a means of treating de Rham cohomology by algebraic methods, as invariants of foliations and pseudogroups of various types, in symplectic and Poisson geometry and, in a more algebraic setting, as algebras of differential operators associated with vector bundles and with infinitesimal actions of Lie groups. These and related differential-geometric structures [1,2,4] make it possible to construct new types of geometric objects on fibered spaces, study their algebro-analytical properties and apply to many problems of mechanics, physics and other natural sciences.
Bibliography
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