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It is shown that the symmetry algebra of quantum superintegrable system can be always chosen to be u(N),N being the number of degrees of freedom., Comment: 8 pages, no figures, a number of examples and references added

We consider local field theory on κ-deformed Minkowski space which is an example of solvable Lie-algebraic noncommutative structure. Using integration formula over κ-Minkowski space and κ-deformed Fourier transform, we consider for deformed local fields the reality conditions as well as deformation of action functionals in standard Minkowski space. We present explicit formulas for two equivalent star products describing CBH quantization of field theory on κ-Minkowski space. We express also via star product technique the noncommutative translations in κ-Minkowski space by commutative translations in standard Minkowski space.

We describe free relativistic fields on noncommutative κ-deformed D=4 Minkowski space. Three possible types of κ-deformed Fourier transforms are discussed, related with three different κ-deformed mass-shell conditions.

The projective representations of k-Galilei group G k are found by contracting the relevant representations of κ–Poincare group. The projective multiplier is found. It is shown that it is not possible to replace the projective representations of G k by vector representations of some its extension.

The representations of the oscillator algebra introduced by Brzezinski et al. [Phys. Lett. B 311 (1993) 202] are classified.

We describe here the general solution describing generators of κ-deformed Poincaré algebra as the functions of classical Poincaré algebra generators as well as the inverse formulas. Further we present analogous relations for the generators of N=1, D=4 κ-deformed Poincaré superalgebra expressed by the classical Poincaré superalgebra generators. In such a way we obtain the κ-deformed Poincaré (super)algebras with all the quantum deformation present only in the co-algebra sector. As an application we use the classical basis of κ-deformed Poincaré superalgebra for obtaining a new result: the κ-deformation of supersymmetric spin (Pauli-Lubanski) Casimir.

The differential realization of the recently proposed deformed Poincaré algebra is considered. The notion of covariant wave functions is introduced and their explicit form in the "minimal" (in Weinberg's sense) case is given. The deformed Dirac equation is constructed.

We consider a particle of half-integer spin which is nonrelativistic in the rest frame. Assuming the particle is completely polarized along third axis we calculate the Bloch vector as seen by a moving observer. The result for its length is expressed in terms of dispersion of some vector operator linear in momentum. The relation with the localization properties is discussed., Comment: 5 pages

A simple theorem concerning the sensitivity of Berry's phases/matrices to the additional degeneracies of the Hamiltonian is proven.

The family of Hamiltonians obtained by the action of a group of canonical transformations is considered. The formula for Hannay's angles is derived which allows us to express them in terms of the geometry of a group. The Berry formula relating Hannay's angles and Berry's phase is rederived.

The bicovariant differential calculus on the four-dimensional kappa-Poincare group and the corresponding Lie-algebra like structure are described. The deifferential calculus on the n-dimensional kappa-Minkowski space covariant under the action of the kappa-Poincare group is constructed., 9 pages,amstex,talk given by P.Maslanka on "IV Colloqium on Quantum Groups and Integrable Models ",Praque'95

The quantum Galilei group $G_{\varkappa}$ is defined. The bicrossproduct structure of $G_{\varkappa}$ and the corresponding Lie algebra is revealed. The projective representations for the two-dimensional quantum Galilei group are constructed., Comment: AMSTeX

We report some results concerning the many-component limit of the gauge Potts model. We find the phase diagrams in the two versions of the model obtained by different coupling of external field.

A particular deformation of central extended Galilei group is considered. It is shown that the deformation influences the rules of constructing the composed systems while one particle states remain basically unaffected. In particular the mass appeared to be non additive., 14 pages LaTeX2e file