Let A be a unital simple separable C*-algebra satisfying the UCT. Assume that dr(A) < +∞, A is Jiang-Su stable, and K0(A)⊗Q ∼= Q. Then A is an ASH algebra (indeed, A is a rationally AH algebra).

The tensor product of vector and arbitrary representations of the nonstandard q-deformation U ′ q(son) of the universal enveloping algebra U(son) of Lie algebra son is defined. The Clebsch– Gordan coefficients of tensor product of vector and arbitrary classical or nonclassical type representations of q-algebra U ′ q(son) are found in an explicit form. The Wigner–Eckart theorem for vector operat...

Several ways to embed q-deformed versions of the Heisenberg algebra into the classical algebra itself are presented. By combination of those embeddings it becomes possible to transform between q-phase-space and q-oscillator realizations of the q-Heisenberg algebra. Using these embeddings the corresponding Schrödinger equation can be expressed by various difference equations. The solutions for t...

We introduce a certain cellular algebra Q(n; r) which is a quotient of the q-Schur algebra S q (n; r). This is naturally equipped with a canonical basis which is compatible with Lusztig's canonical bases for certain modules for the quantized enveloping algebra U (sl n). We describe a diagram calculus for Q(n; r) which makes calculations involving the corresponding canonical bases easy to unders...

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

We construct cocycles on the Lie algebra of pseudoand q-pseudodifferential symbols of one variable and on their close relatives: the sine-algebra and the Poisson algebra on two-torus. A ``quantum'' Godbillon Vey cocycle on (pseudo)differential operators appears in this construction as a natural generalization of the Gelfand Fuchs 3-cocycle on periodic vector fields. A nontrivial embedding of th...

Introducing an H-Hopf algebroid structure into Uq,p(ŝl2), we investigate the vertex operators of the elliptic quantum group Uq,p(ŝl2) defined as intertwining operators of infinite dimensional Uq,p(ŝl2)-modules. We show that the vertex operators coincide with the previous results obtained indirectly by using the quasi-Hopf algebra Bq,λ(ŝl2). This shows a consistency of our H-Hopf algebroid struc...

In this paper, we show the second part of Schur-Weyl duality for mixed tensor space. The quantum group U = U(gln) of the general linear group and a q-deformation Br,s(q) of the walled Brauer algebra act on V ⊗r ⊗V ∗⊗s where V = R is the natural U-module. We show that EndBnr,s(q)(V ⊗r ⊗ V ∗) is the image of the representation of U, which we call the rational q-Schur algebra. As a byproduct, we o...

An extra term generally appears in the q-deformed su(2) algebra for the deformation parameter q = exp 2πiθ, if one combines the Biedenharn-Macfarlane construction of q-deformed su(2), which is a generalization of Schwinger’s construction of conventional su(2), with the representation of the q-deformed oscillator algebra which is manifestly free of negative norm. This extra term introduced by th...