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...

The resulting algebra is known as the Hall algebra HA of A. Hall algebras first appeared in the work of Steinitz [S] and Hall [H] in the case where A is the category of Abelian p-groups. They reemerged in the work of Ringel [R1]-[R3], who showed in [R1] that when A is the category of quiver representations of an A-D-E quiver ~ Q over a finite field Fq, the Hall algebra of A provides a realizati...

in this paper, we represent an inexact inverse subspace iteration method for com- puting 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.

These rings admit numerous algebraic and geometric realizations, but one of the historically first constructions, which dates back to the work of Steinitz in 1900 and later completed by Hall, was given in terms of what is now called the classical Hall algebra H (see [Ma], Chapter III ). This algebra has a basis consisting of isomorphism classes of abelian q-groups, where q is a fixed prime powe...

In this paper, a new notion, called TM-algebra, which is a generalization of the idea of Q/BCH/BCI/BCK/BCC-algebra, is introduced. Some theorems discussed in Q-and BCK algebras are generalized. Definition of TM-algebra along with various propositions are stipulated and presented with their respective proofs. The relation between TM-algebra and other algebra has been investigated and detailed in...

Let q be a Lie algebra over an algebraically closed field k of characteristic zero. The symmetric algebra S(q) has a natural structure of Poisson algebra, and our goal is to present a sufficient condition for the maximality of Poisson-commutative subalgebras of S(q) obtained by the argument shift method. Study of Poisson-commuttive subalgebras of S(q) has attracted much attention in the last ye...

Let F denote a field, and fix a nonzero q ∈ F such that q 6= 1. The universal Askey–Wilson algebra is the associative F-algebra ∆ = ∆q defined 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 ∆. In this paper we discuss a connection between ∆ ...

We give a presentation of the endomorphism algebra EndUq(sl2)(V ), where V is the 3-dimensional irreducible module for quantum sl2 over the function field C(q 1 2 ). This will be as a quotient of the Birman-Wenzl-Murakami algebra BMWr(q) := BMWr(q , q2− q) by an ideal generated by a single idempotent Φq. Our presentation is in analogy with the case where V is replaced by the 2dimensional irredu...

The quantum double construction of a q-deformed boson algebra possessing a Hopf algebra structure is carried out explicitly. The R-matrix thus obtained is compared with the existing literature. Recently there has been an increasing interest in the deformation of Lie (super)algebras[1, 2, 3, 4, 5, 6] and their quasitriangular Hopf algebra nature[7], mainly because of there wide applications in m...