ﻻ يوجد ملخص باللغة العربية
A version of the twisted Poincar{e} duality is proved between the Poisson homology and cohomology of a polynomial Poisson algebra with values in an arbitrary Poisson module. The duality is achieved by twisting the Poisson module structure in a canonical way, which is constructed from the modular derivation. In the case that the Poisson structure is unimodular, the twisted Poincar{e} duality reduces to the Poincar{e} duality in the usual sense. The main result generalizes the work of Launois-Richard cite{LR} for the quadratic Poisson structures and Zhu cite{Zhu} for the linear Poisson structures.
A duality between an electrostatic problem in a three dimensional world and a quantum mechanical problem in a one dimensional world which allows one to obtain the ground state solution of the Schrodinger equation by using electrostatic results is gen
The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally compact topologi
We generalize the notion of weight for Gelfand-Fuks cohomology theory of symplectic vector spaces to the homogeneous Poisson vector spaces, and try some combinatorial approach to Poisson cohomology groups.
We introduce the notion of weakly associative algebra and its relations with the notion of nonassociative Poisson algebras.
We give an explicit formula showing how the double Poisson algebra introduced in cite{VdB} appears as a particular part of a pre-Calabi-Yau structure, i.e. cyclically invariant, with respect to the natural inner form, solution of the Maurer-Cartan eq