The quantum algebra su q (2) is introduced as a deformation of the ordinary Lie algebra su(2). This is achieved in a simple way by making use of q-bosons. In connection with the quantum algebra su q (2), we discuss the q-analogues of the harmonic oscillator and the angular momentum. We also introduce q-analogues of the hydrogen atom by means of a q-deformation of the Pauli equations and of the ...

Let V m,n p,q be the irreducible representation of the Virasoro algebra L with central charge cp,q = 1− 6(p − q) /pq and highest weight hm,n = [(np−mq)−(p−q)]/4pq, where p, q > 1 are relatively prime integers, and m, n are integers, such that 0 < m < p, 0 < n < q. For fixed p and q the representations V m,n p,q form the (p, q) minimal model of the Virasoro algebra [1]. For N > 0 let LN be the L...

It is well-known that the Macfarlane-Biedenharn q-oscillator and its generalization has no Hopf structure, whereas the Hong Yan q-oscillator can be endowed with a Hopf structure. In this letter, we demonstrate that it is possible to construct a general q-oscillator algebra which includes the Macfarlane-Biedenharn oscillator algebra and the Hong Yan oscillator algebra as special cases. E-mail ad...

‎Our aim in this very short note is to show that the proof of the‎ ‎following well-known fundamental lemma of Zariski follows from an‎ ‎argument similar to the proof of the fact that the rational field‎ ‎$mathbb{Q}$ is not a finitely generated $mathbb{Z}$-algebra.

This paper studies a q-deformation, Br,s(q), of the walled Brauer algebra (a certain subalgebra of the Brauer algebra) and shows that the centralizer algebra for the action of the quantum group UR(gln) on mixed tensor space (R) ⊗ (Rn)∗ is generated by the action of Br,s(q) for any commutative ring R with one and an invertible element q.

Capparis spinosa L. has many biological effects such as antioxidant properties. In the present study, we compared the effects of the hydro-alcoholic extract of Capparis spinosa fruit, quercetin (Q), and vitamin E (Vit E) on monosodium glutamate (MSG)-induced toxicity. The following groups were designed: Control groups (normal saline and/or corn oil); MSG group (4.00 g kg-...

In a recent work [FR], Frenkel and Reshetikhin developed the theory of q-vertex operators. They showed that n-point correlation functions associated to q-vertex operators satisfy a qdifference equation called q-deformed Kniznik-Zamolodchikov equation. In the derivation of this equation, a crucial point is that the quantum affine algebra is a quasi-triangular Hopf algebra. By using several prope...

Let F denote a field, and let V vector space over with finite positive dimension. We consider an ordered pair of -linear maps A : ? ? such that (i) each , is diagonalizable; (ii) there exists ordering { i } = 0 d the eigenspaces ? ? 1 + for ? where ; (iii) ? (iv) does not exist subspace U ? . call tridiagonal on assume belongs to family pairs said have q -Racah type. There infinite-dimensional ...