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...

Frenkel-Reshetikhin introduced q-characters of finite dimensional representations of quantum affine algebras [6]. We give a combinatorial algorithm to compute them for all simple modules. Our tool is t-analogue of the q-characters, which is similar to Kazhdan-Lusztig polynomials, and our algorithm has a resemblance with their definition. We need the theory of quiver varieties for the definition...

Given a finite quiver Q without loops, we introduce a new class of quantum algebras D(Q) which are deformations of the enveloping algebra of a Lie algebra which is a central extension of sln(Π(Q)) where Π(Q) is the preprojective algebra of Q. When Q is an affine Dynkin quiver of type A, D or E, we can relate them to Γ-deformed double current algebras. We are able to construct functors between d...

Recently B. Hartwig and the second author found a presentation for the three-point sl2 loop algebra via generators and relations. To obtain this presentation they defined an algebra ⊠ by generators and relations, and displayed an isomorphism from ⊠ to the three-point sl2 loop algebra. We introduce a quantum analog of ⊠ which we call ⊠q. We define ⊠q via generators and relations. We show how ⊠q ...

We show that every Lie algebra or superLie algebra has a canonical braiding on it, and that in terms of this its enveloping algebra appears as a flat space with braided-commuting coordinate functions. This also gives a new point of view about q-Minkowski space which arises in a similar way as the enveloping algebra of the braided Lie algebra gl2,q. Our point of view fixes the signature of the m...

Macrocycles and p-benzoquinones (p-BQ) have been generally connected as potential co-synergist redox models in aerobic oxidation. To get insight for the synergist oxidation of hydroquinones (H2Q), thus, we synthesized and characterized dibenzotetraaza [14]annulene type macrocycles of FeIII and CoII metal ions and described by utilizing different examinations inc...

An algebra is introduced which can be considered as a rank 2 extension of the Askey-Wilson algebra. Relations in this are motivated by relations between coproducts twisted primitive elements two-fold tensor product quantum $\mathcal{U}_{q}(\mathfrak{sl}(2,\mathbb C))$. It shown that bivariate $q$-Racah polynomials appear overlap coefficients eigenvectors generators Furthermore, corresponding $q...

The R12 h matrices of the Jordanian Uh(sl(2)) algebra at arbitrary dimensions may be obtained from the corresponding Rj1;j2 q matrices of the standard q-deformed Uq(sl(2)) algebra through a contraction technique. By extending this method, the coloured two-parametric (h, α) Jordanian R1122 h,α matrices of the Uh,α(gl(2)) algebra may be derived from the corresponding coloured R j1,z1;j2,z2 q,λ ma...

We introduce a new family of superalgebras, the quantum walled Brauer-Clifford superalgebras BCr,s(q). The superalgebra BCr,s(q) is a quantum deformation of the walled BrauerClifford superalgebra BCr,s and a super version of the quantum walled Brauer algebra. We prove that BCr,s(q) is the centralizer superalgebra of the action of Uq(q(n)) on the mixed tensor space V q = V ⊗r q ⊗ (V∗ q) when n ≥...

is surjective. If W is a Q-vector space, Q-algebra or Q-Lie algebra then we write WC for the correspondingC-vector space (respectively, C-algebra orC-Lie algebra) W ⊗Q C. Let f(x) ∈ C[x] be a polynomial of degree n ≥ 2 without multiple roots. Suppose that p is a prime that does not divide n and a positive integer q = p is a power of p. As usual, φ(q) = (p − 1)p denotes the Euler function. Let u...