A Generalization of the Stone–Von Neumann Theorem to Nonregular Representations of the CCR-Algebra

We give a classification, up to unitary equivalence, of the representations of the C*-algebra of the Canonical Commutation Relations which generalizes the classical Stone–von Neumann Theorem to the case of representations which are strongly measurable, but not necessarily strongly continuous. The classification includes all the (nonregular) representations which have been considered in physical models.     

Some Remarks on the Cohomology of Krichever–Novikov Algebras

We calculate the continuous cohomology of the Lie algebra of meromorphic vector fields on a compact Riemann surface from the cohomology of the holomorphic vector fields on the open Riemann surface pointed in the poles. This cohomology has been given by Kawazumi. Our result shows the Feigin–Novikov conjecture.     

ALGEBRAIC METHOD FOR VIBRATIONAL ENERGY SPECTRA OF H 2O AND NO 2

文内提出一种研究Ｈ２Ｏ和ＮＯ２高激发伸缩振动的Ｕ（２）代数模型,在极限条件下,该模型退化为一种非谐和耦合的局域模模型,用该模型的六个可调参数拟合实验数据,算得的标准偏差比相应的非谐和耦合的局域模型算得的偏差要小     

Gauss Decomposition of Dynamical Elliptic Algebra Aq,p,π(gln)

We propose a dynamical elliptic algebra which is based on the relations RLL = LLR^*, where R and R^* are the dynamical R-matrices of A_n-1⁽¹⁾-type face model with the elliptic module shifted by the center of algebra. nom the high-rank Gauss decomposition,h we obtain the Drinfeld currents of dynarnical elliptic algebra .     

Duality for Coloured Quantum Groups

Duality between the coloured quantum group and the coloured quantum algebra corresponding to GL(2) is established. The coloured L ^± functionals are constructed and the dual algebra is derived explicitly. These functionals are then employed to give a coloured generalisation of the differential calculus on quantum GL(2) within the framework of the R-matrix approach.     

Covering and gluing of algebras and differential algebras

Extending work of Budzyński and Kondracki, we investigate coverings and gluings of algebras and differential algebras. We describe in detail the gluing of two quantum discs along their classical subspace, giving a C^*-algebra isomorphic to a certain Podleś sphere, as well as the gluing of U_q^1/2(sl₂)-covariant differential calculi on the discs.     

Weakly o‐Minimal Expansions of Boolean Algebras

We propose a definition of weak o‐minimality for structures expanding a Boolean algebra. We study this notion, in particular we show that there exist weakly o‐minimal non o‐minimal examples in this setting.     

Power series with rational coefficients for two-electron atom energies

The method of o(4, 2) operator replacements is generalized. As a result, the series whose limiting values when the variable goes to +∞ should correspond to the two-electron atom energies now have rational coefficients. This generalization allows one also to compute the series for the case of singlet S symmetry, a case which could not be considered in the previous original formulation of the method. Series with rational coefficients for the helium singlet and triplet S ground-state energy are calculated up to order 41 and 45, respectively. Moreover, symbolic computations also allow one to give the first few coefficients of these series for arbitrary values of the nuclear charge Z. Finally, a new method for analytic continuation to the limit +∞ is presented for the energies of the helium singlet and triplet ground states. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63 : 1079–1089, 1997