A convenient criterion under which Z_2-graded operators are Hamiltonian

We formulate a simple and convenient criterion under which skew-adjoint Z_2-graded total differential operators are Hamiltonian, provided that their images are closed under commutation in the Lie algebras of evolutionary vector fields on the infinite jet spaces for vector bundles over smooth manifolds.Comment: J.Phys.Conf.Ser.: Mathematical and Physical Aspects of Symmetry. Proc. 28th Int. colloq. on group-theoretical methods in Physics (July 26-30, 2010; Newcastle-upon-Tyne, UK), 6 pages (in press

Bimodule structure of the mixed tensor product over Uqsℓ(2∣1)U_{q} s\ell(2|1) and quantum walled Brauer algebra

We study a mixed tensor product $\mathbf{3}^{\otimes m} \otimes \mathbf{\overline{3}}^{\otimes n}$ of the three-dimensional fundamental representations of the Hopf algebra $U_{q} s\ell(2|1)$, whenever $q$ is not a root of unity. Formulas for the decomposition of tensor products of any simple and projective $U_{q} s\ell(2|1)$-module with the generating modules $\mathbf{3}$ and $\mathbf{\overline{3}}$ are obtained. The centralizer of $U_{q} s\ell(2|1)$ on the chain is calculated. It is shown to be the quotient $\mathscr{X}_{m,n}$ of the quantum walled Brauer algebra. The structure of projective modules over $\mathscr{X}_{m,n}$ is written down explicitly. It is known that the walled Brauer algebras form an infinite tower. We have calculated the corresponding restriction functors on simple and projective modules over $\mathscr{X}_{m,n}$. This result forms a crucial step in decomposition of the mixed tensor product as a bimodule over $\mathscr{X}_{m,n}\boxtimes U_{q} s\ell(2|1)$. We give an explicit bimodule structure for all $m,n$.Comment: 43 pages, 5 figure

On the variational noncommutative Poisson geometry

We outline the notions and concepts of the calculus of variational multivectors within the Poisson formalism over the spaces of infinite jets of mappings from commutative (non)graded smooth manifolds to the factors of noncommutative associative algebras over the equivalence under cyclic permutations of the letters in the associative words. We state the basic properties of the variational Schouten bracket and derive an interesting criterion for (non)commutative differential operators to be Hamiltonian (and thus determine the (non)commutative Poisson structures). We place the noncommutative jet-bundle construction at hand in the context of the quantum string theory.Comment: Proc. Int. workshop SQS'11 `Supersymmetry and Quantum Symmetries' (July 18-23, 2011; JINR Dubna, Russia), 4 page

Lifetimes of Xi_{bc}^{+} and Xi_{bc}^{0} baryons

Estimates of lifetimes and partial branching ratios for the baryons $\Xi_{bc}^{+}$ and $\Xi_{bc}^{0}$ are presented using the inverse heavy quark mass expansion technique carried out in the Operator Product Expansion approach. We take into account both the perturbative QCD corrections to the spectator contributions and, depending on the quark contents of hadrons, the Pauli interference and weak scattering effects between the constituents, using a potential model for the evaluation of the non-perturbative parameters.Comment: 15 pages, LATEX file, 2 eps-figure