Hilbert space representations of the cross product ∗-algebras of the Hopf ∗-algebra Uq(su2) and its module ∗-algebras O(Sqr) of Podleś spheres are investigated and classified by describing the action of generators. The representations are analyzed within two approaches. It is shown that the Hopf ∗-algebra O(SUq(2)) of the quantum group SUq(2) decomposes into an orthogonal sum of projective Hopf...

The first has to do with skew invariant theory. Let V be a finite dimensional complex vector space with a skew symmetric non-degenerate form and let Sp(V ) be the corresponding symplectic group. For a complex vector space W we consider the action of Sp(V ) on the exterior algebra Λ(V ⊗W ) (the action being trivial on W ). In Theorem 2.3 we give generators and relations for the algebra of Sp(V )...

Hilbert space representations of the cross product ∗-algebras of the Hopf ∗-algebra Uq(su2) and its module ∗-algebras O(Sqr) of Podleś spheres are investigated and classified by describing the action of generators. The representations are analyzed within two approaches. It is shown that the Hopf ∗-algebra O(SUq(2)) of the quantum group SUq(2) decomposes into an orthogonal sum of projective Hopf...

Hilbert space representations of the cross product ∗-algebras of the Hopf ∗-algebra Uq(su2) and its module ∗-algebras O(Sqr) of Podles’ spheres are investigated and classified by describing the action of generators. The representations are analyzed within two approaches. It is shown that the Hopf ∗-algebra O(SUq(2)) of the quantum group SUq(2) decomposes into an orthogonal sum of projective Hop...

The aim of this paper is to elucidate the role played by the bosonic/fermionic character of N He atoms solvating a Br2(X) molecule. To this end, an adiabatic model in the molecular stretching coordinate is assumed and the ground energy levels of the complexes are searched by means of Hartree (or Hartree-Fock) Quantum Chemistry calculations for 4He (or 3He) solvent atoms. Simulations of vib-rota...

The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the Schwinger oscillator construction for SU(2), and its relevance in several quantum mechanical contexts is highlighted. The Schwinger representations for SU(2), SO(...

The importance of frustration and disorder is well known to condensed-matter physicists working in the field of spin-glasses and related systems [1]. In these systems one can find a variety of “unusual” phases which, in some cases, present completely new phenomena (for example, the existence of a multiplicity of vacua not related by a symmetry of the action). It is interesting to ask whether si...

As an attempt to bridge between numerical analysis and algebraic geometry, this paper formulates the multiplicity for the general nonlinear system at an isolated zero, presents an algorithm for computing the multiplicity structure, proposes a depth-deflation method for accurate computation of multiple zeros, and introduces the basic algebraic theory of the multiplicity. Furthermore, this paper ...

our main objective is a better understanding of spin spin interaction of dinuclear copper(ii) complexes through  system. the synthesis and characterization of two new dinuclear copper(ii) complexes, based on the use of large, pyrole-containing macrocycles, the so called “ expanded porphyrins” , [cu2(macrocycle)]4+ is described. a chloroform solution spectrum of two complexes taken at room tem...