For the quantum group GLp,q(2) and the corresponding quantum algebra Up,q(gl(2)) Fronsdal and Galindo [1] explicitly constructed the so-called universal T -matrix. In a previous paper [2] we showed how this universal T -matrix can be used to exponentiate representations from the quantum algebra to get representations (left comodules) for the quantum group. Here, further properties of the univer...

Let F denote a field, and fix a nonzero q ∈ F such that q 6= 1. We define an associative F-algebra ∆ = ∆q by generators and relations in the following way. The generators are A, B, C. The relations assert that each of A+ qBC − q−1CB q2 − q−2 , B + qCA− q−1AC q2 − q−2 , C + qAB − q−1BA q2 − q−2 is central in ∆. We call ∆ the universal Askey–Wilson algebra. We discuss how ∆ is related to the orig...

We represent every normal-valued GMV-algebra as a GMV-algebra of real-valued functions; we also describe the universal MV-algebras and universal normal-valued GMV-algebras with a prescribed set of components.

The paper is devoted to concern a relationship between rough set theory and universal algebra. Notions of lower and upper rough approximations on an algebraic structure induced by an ideal are introduced and some of their properties are studied. Also, notions of rough subalgebras and rough ideals with respect to an ideal of an algebraic structure, which is an extended notion of subalgebras and ...

Contracting the h-deformation of SL(2, R), we construct a new deformation of two dimensional Poincaré algebra, the algebra of functions on its group and its differential structure. It is also shown that the Hopf algebra is triangular, and its universal R matrix is also constructed explicitly. Then, we find a deformation map for the universal enveloping algebra, and at the end, give the deformed...

The number of distinct operations (that is, the range of the variable a) may be infinite, but for our main result (Theorem 2), we shall require every n(a) to be finite—that is, it will concern algebras with finitary operations. The concepts of subalgebra, congruence relation on an algebra, homomorphism of one algebra A onto (or into) another algebra with the same operations, and of the direct u...