The notion of a Poisson algebra was probably introduced in the first time by A.M. Vinogradov and J. S. Krasil’shchik 1975 under name “canonical algebra” Braconnier his short note “Algèbres de Poisson” (Comptes rendus Ac.Sci) 1977.

The commutative algebra of all canonical affinor structures on homogeneous k-symmetric spaces is completely described. It gives a classification of these spaces with respect to the algebra.

The standard geometrodynamics is reformulated into a theory of conformal geometrodynamics by extending the ADM phase space for canonical general relativity to a phase space consisting of York’s exterior mean curvature time, conformal 3-metric and their momenta. Accordingly, an additional constraint is introduced, called the conformal constraint. In terms of the new canonical variables, a diffeo...

A constraint satisfaction problem has compactness if any infinite set of constraints is satisfiable whenever all its finite subsets are satisfiable. We prove a sufficient condition for compactness, which holds for a range of problems including those based on the well-known Interval Algebra (IA) and RCC8. Furthermore, we show that compactness leads to a useful necessary and sufficient condition ...

We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the algebra by linear transformation of coordinates and transmitted to the Hamiltonian (Lagrangian). Since linear transformations do not change the quadratic form of ...

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded...

We describe a method for an explicit determination of indecomposable preprojective and preinjective representations for extended Dynkin quivers Γ over an arbitrary field K by vector spaces and matrices. This method uses tilting theory and the explicit knowledge of indecomposable modules over the corresponding canonical algebra of domestic type. Further, if K is algebraically closed we obtain al...

Classical and quantum mechanics for an extended Heisenberg algebra with canonical commutation relations for position and momentum coordinates are considered. In this approach additional noncommutativity is removed from the algebra by linear transformation of phase space coordinates and transmitted to the Hamiltonian (Lagrangian). This transformation does not change the quadratic form of Hamilto...

We extend the canonical commutation relations (CCR) in quantum mechanics to the case where appropriate dynamical variables are angular momenta and angles. It is found that projection operators of the resultant Weyl algebra provide us with a new and powerful way of characterizing minimum uncertainty states, including those obtained by Carruthers and Nieto. The uniqueness theorem of Schrodinger r...

By using a framework where the object of noncommutativity θ represents independent degrees of freedom, we study the symmetry properties of an extended x + θ space-time, given by the group P ’, which has the Poincaré group P as a subgroup. In this process we use the minimal canonical extension of the Doplicher, Fredenhagen and Roberts algebra. It is also proposed a generalized Dirac equation, wh...