340 research outputs found
Quadratic Poisson brackets and Drinfeld theory for associative algebras
The paper is devoted to the Poisson brackets compatible with multiplication
in associative algebras. These brackets are shown to be quadratic and their
relations with the classical Yang--Baxter equation are revealed. The paper also
contains a description of Poisson Lie structures on Lie groups whose Lie
algebras are adjacent to an associative structure.Comment: 16 pages, latex, no figure
On the algebraic structures connected with the linear Poisson brackets of hydrodynamics type
The generalized form of the Kac formula for Verma modules associated with
linear brackets of hydrodynamics type is proposed. Second cohomology groups of
the generalized Virasoro algebras are calculated. Connection of the central
extensions with the problem of quntization of hydrodynamics brackets is
demonstrated
Quadratic Poisson brackets and Drinfel'd theory for associative algebras
Quadratic Poisson brackets on associative algebras are studied. Such a
bracket compatible with the multiplication is related to a differentiation in
tensor square of the underlying algebra. Jacobi identity means that this
differentiation satisfies a classical Yang--Baxter equation. Corresponding Lie
groups are canonically equipped with a Poisson Lie structure. A way to quantize
such structures is suggested.Comment: latex, no figures
On the virial theorem for the relativistic operator of Brown and Ravenhall, and the absence of embedded eigenvalues
A virial theorem is established for the operator proposed by Brown and
Ravenhall as a model for relativistic one-electron atoms. As a consequence, it
is proved that the operator has no eigenvalues greater than , where is the fine structure constant, for
all values of the nuclear charge below the critical value : in
particular there are no eigenvalues embedded in the essential spectrum when . Implications for the operators in the partial wave
decomposition are also described.Comment: To appear in Letters in Math. Physic
Dirac-Sobolev inequalities and estimates for the zero modes of massless Dirac operators
The paper analyses the decay of any zero modes that might exist for a
massless Dirac operator H:= \ba \cdot (1/i) \bgrad + Q, where is -matrix-valued and of order O(|\x|^{-1}) at infinity. The approach
is based on inversion with respect to the unit sphere in and
establishing embedding theorems for Dirac-Sobolev spaces of spinors which
are such that and lie in Comment: 11 page
Hydrodynamic chains and a classification of their Poisson brackets
Necessary and sufficient conditions for an existence of the Poisson brackets
significantly simplify in the Liouville coordinates. The corresponding
equations can be integrated. Thus, a description of local Hamiltonian
structures is a first step in a description of integrable hydrodynamic chains.
The concept of Poisson bracket is introduced. Several new Poisson brackets
are presented
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