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Noncommutative Symplectic Geometry of the Endomorphism Algebra of a Vector Bundle
Zakaria Giunashvili
We study noncommutative generalizations of such notions of the classical symplectic geometry as degenerate Poisson structure, Poisson submanifold and quotient manifold, symplectic…
Hamiltonian Systems on Complex Grassmann Manifold. Holonomy and Schrodinger Equation
Zakaria Giunashvili
Differential geometric structures such as the principal bundle for the canonical vector bundle on a complex Grassmann manifold, the canonical connection form on this bundle, the ca…
The Characteristic Class of a Lie Algebra Ideal, Contact Structures and the Poisson Algebra of Basic Functions
Zakaria Giunashvili
Some cohomology classes associated with an ideal in a Lie algebra, a Poisson structure on the basic functions algebra of contact structure, its Poisson cohomology and geometric (pr…
Noncommutative Geometry of Phase Space
Zakaria Giunashvili
We investigate the geometric, algebraic and homologic structures related with Poisson structure on a smooth manifold. Introduce a noncommutative foundations of these structures for…