It is shown that there exists an isomorphism between q-oscillator systems covariant under SUq(n) and SUq−1(n). By the isomorphism, the defining relations of SUq−1(n) covariant q-oscillator system are transmuted into those of SUq(n). It is also shown that the similar isomorphism exists for the system of q-oscillators covariant under the quantum supergroup SUq(n/m). Furthermore the cases of q-def...

For a regular κ, a partial ordering P is said to have the κ Freese-Nation property (the κ-FN for short) if there is a mapping (κ-FN mapping) f : P → [P ] such that for any p, q ∈ P if p ≤ q then there is r ∈ f(p) ∩ f(q) such that p ≤ r ≤ q. Freese and Nation [5] used the א0-FN in a characterization of projective lattices and asked if this property alone already characterizes the projectiveness....

S-Heun operators on linear and $q$-linear grids are introduced. These special cases of Heun related to Sklyanin-like algebras. The Continuous Hahn Big $q$-Jacobi polynomials functions which these have natural actions. We show that the encompass both bispectral Kalnins Miller's structure operators. four realize limit trigonometric degeneration original Sklyanin algebra. Finite-dimensional repres...

We write the fermionic q-Fock space representation of Uq(ŝln) as an infinite extended braided tensor product of finite-dimensional fermionic Uq(sln)-quantum planes or exterior algebras. Using braided geometrical techniques developed for such quantum exterior algebras, we provide a new approach to the Kashiwara-Miwa-Stern action of the Heisenberg algebra on the q-fermionic Fock space, obtaining ...

We review some aspects of the relation between ordinary coherent states and q-deformed generalized coherent states with some of the simplest cases of quantum Lie algebras. In particular, new properties of (q-)coherent states are utilized to provide a path integral formalism allowing to study a modified form of q-classical mechanics, to probe some geometrical consequences of the q-deformation an...

Let B be a complex unital Banach algebra. We consider the Banach algebra A = B × C ordered by the algebra cone K = {(a, ξ) ∈ A : ‖a‖ ≤ ξ}, and investigate the connection between results on ordered Banach algebras and the right bound of the numerical range of elements in B. 1. Ordered Banach algebras The aim of this paper is to stress the aspect of the applicability of the ordered Banach algebra...

We have two polynomial time results for the uniform word problem for a quasivariety Q: (a) The uniform word problem for Q can be solved in polynomial time iff one can find a certain congruence on finite partial algebras in polynomial time. (b) Let Q* be the relational class determined by Q. If any universal Horn class between the universal closure S(Q*) and the weak embedding closure S(Q*) of Q...

for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

Ordered sheaves on a small quantaloid Q have been defined in terms of Qenriched categorical structures; they form a locally ordered category Ord(Q). The free-cocompletion KZ-doctrine on Ord(Q) has Mod(Q), the quantaloid of Q-modules, as category of Eilenberg-Moore algebras. In this paper we give an intrinsic description of the Kleisli algebras: we call them the locally principally generated Q-m...

We consider algebras eiΠ λ(Q)ei obtained from deformed preprojective algebra of affine type Π(Q) and an idempotent ei for certain concrete value of the vector λ which corresponds to the traces of −1 ∈ SU(2,C) in irreducible representations of finite subgroups of SU(2,C). We give a certain realization of these algebras which allows us to construct the C∗-enveloping algebras for them. Some well-k...