‎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.

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 ...

We describe properties of the nonstandard q-deformation U ′ q (son) of the universal enveloping algebra U (son) of the Lie algebra son which does not coincide with the Drinfeld–Jimbo quantum algebra Uq(son). In particular, it is shown that there exists an isomorphism from U ′ q (son) to Uq(sln) and that finite dimensional ir-reducible representations of U ′ q (son) separate elements of this alg...

The various relations between q-deformed oscillators algebras and the q-deformed su(2) algebras are discussed. In particular, we exhibit the similarity of the q-deformed su(2) algebra obtained from q-oscillators via Schwinger construction and those obtained from q-Holstein-Primakoff transformation and show how the relation between su √ q (2) and Hong Yan q-oscillator can be regarded as an speci...