Isometric embedding for homogeneous compact 3-manifolds

The anisotropic homogeneous ³ is isometrically globally embedded into a nine-dimensional Euclidean or pseudo-Euclidean space. In a special case the Euclidean space is six-dimensional. The space-sections of the anti-Mach metric appear as a submanifold of theE ⁹. We obtain also the isometric embedding ofSO(3) with its natural Killing metric.     

Boson realization of YangiansY(sl(2)) andY(sl(3))

Studying the algebraic structure of the YangiansY(sl(2)), andY(sl(3)) we present their boson realizations. In the case ofY(sl(2)) we give the realization by using 1-canonical boson pair and two parameters and in theY(sl(3)) with 2-canonical boson pairs, two parameters and subalgebrasl(2). Substituting the realization ofU(sl(2)), we can obtain the pure boson realization by 3-canonical pairs and three parameters.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.     

Theq-calculus for genericq andq a root of unity

Theq-calculus for genericq is developed and related to the deformed oscillator of parameterq ^1/2. By passing with care to the limit in whichq is a root of unity, one uncovers the full algebraic structure ofZ _n -graded fractional supersymmetry and its natural representation.Presented at the 5th International Colloquium on Quantum Groups: Quantum Groups and Integrable Systems, Prague, 20–22 June 1996.This paper describes research supported in part by E.P.S.R.C and P.P.A.R.C. (UK) and by the C.I.C.Y.T (Spain). J.C.P.B. wishes to acknowledge an FPI grant from the CSIC and the Spanish Ministry of Education and Science.     

137-01137-01137-01-deformed extended Galilei algebra

We apply the pseudoextension mechanism, which in the undeformed case gives the centrally extended Galilei group {ie137-02} as a contraction of a trivial extensionP×U(1) of the Poincaré group, to the case of the-Poincaré algebra. As a result, the four-dimensional {ie137-03}-deformed extended Galilei algebra is obtained.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.     

Resonances in low-energy rare-gas atom scattering

Precise values of energies and widths of low-lying resonances in some rare-gas atom systems (Ar-Ar, Ne-Kr, Ne-Xe) are reported.