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...

A subspace of matrices in F m×n qe can be naturally embedded as a xmlns:xlink="http://www.w3.org/1999/xlink">em×en xmlns:xlink="http://www.w3.org/1999/xlink">q with the property...

I consider the Diophantine approximation problem of sup-norm simultaneous rational approximation with common denominator of a pair of irrational numbers, and compute explicitly some pairs with large approximation constant. One of these pairs is the most badly approximable pair yet computed. The theory of approximation of a single irrational number by rationals is well known, and for our purpose...

When the parameter q ∈ C is not a root of unity, simple modules of affine q-Schur algebras have been classified in terms of Frenkel–Mukhin’s dominant Drinfeld polynomials ([6, 4.6.8]). We compute these Drinfeld polynomials associated with the simple modules of an affine q-Schur algebra which come from the simple modules of the corresponding q-Schur algebra via the evaluation maps.

Let $q$ be a nonzero complex number that is not root of unity. In the $q$-oscillator with commutation relation $ a^+-qa^+ =1$, it known smallest commutator algebra operators containing creation and annihilation $a^+$ linear span $, together all form ${a^+}^l{\left[a,a^+\right]}^k$, ${\left[a,a^+\right]}^k ^l$, where $l$ nonnegative integer $k$ positive integer. That is, combinations ^h$ or $(a^...

Starting with a given generalized boson algebra U〈q〉(h(1)) known as the bosonized version of the quantum super-Hopf Uq(osp(1|2)) algebra, we employ the Hopf duality arguments to provide the dually conjugate function algebra Fun〈q〉(H(1)). Both the Hopf algebras being finitely generated, we produce a closed form expression of the universal T matrix that caps the duality and generalizes the famili...

let $f_q d_{2n}$ be the group algebra of $d_{2n}$, the dihedral group of order $2n$ over $f_q=gf(q)$. in this paper, we establish the structure of $u(f_{2^k}d_{2n})$, the unit group of $f_{2^k}d_{2n}$ and that of its normalized unitary subgroup $v_*(f_{2^k}d_{2n})$ with respect to canonical involution $*$ when $n$ is odd.

Let C denote the algebra of functions continuous on the unit circle. With norm ||/¡| =sup¡xi-i \f(X)\, C is a Banach algebra. Let A denote the set of all / in C which are boundary values of functions analytic in \z\ <1 and continuous in \z\ ál. A is then a closed subalgebra of C, and by known results A consists of those and only those/ in C for which /|X|-l/(X)XBdX = 0, «^0. In [l ] the questio...