in this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)d^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the banach algebras. this proof is given in two cases of the continuous and discontinuous function $g$, under the generalized lipschitz and caratheodory conditions.

Quantum Lie algebras (an important class of quadratic algebras arising in the Woronowicz calculus on quantum groups) are generalizations of Lie (super) algebras. Many notions from the theory of Lie (super)algebras admit “quantum” generalizations. In particular, there is a BRST operator Q (Q2 = 0) which generates the differential in the Woronowicz theory and gives information about (co)homologie...

In this paper, we construct the Heisenberg–Virasoro algebra in framework of R(p,q)-deformed quantum algebras. Moreover, R(p,q)-Heisenberg–Witt n-algebras is also investigated. Furthermore, generalize notion elliptic Hermitian matrix models. We use constraints to evaluate R(p,q)-differential operators Virasoro and it higher order differential operators. Particular cases corresponding algebras ex...

This paper provides a survey for the latest developments in the theory of affine q-Schur algebras and Schur–Weyl duality between affine quantum gln and affine type A Hecke algebras. More precisely, we will establish, on the one side, an isomorphism between the double Ringel–Hall algebra D△(n) of a cyclic quiver △(n) and the quantum loop algebra of gln, and establish, on the other side, explicit...

We show that, over an arbitrary field, q-rook monoid algebras are iterated inflations of Iwahori-Hecke algebras, and, in particular, are cellular. Furthermore we give an algebra decomposition which shows a q-rook monoid algebra is Morita equivalent to a direct sum of Iwahori-Hecke algebras. We state some of the consequences for the representation theory of q-rook monoid algebras.

‎we obtain the porc formulae for the number of non-associative algebras‎ ‎of dimension 2‎, ‎3 and 4 over the finite field gf$(q)$‎. ‎we also give some‎ ‎asymptotic bounds for the number of algebras of dimension $n$ over gf$(q)$.

In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function $g$, under the generalized Lipschitz and Caratheodory conditions.

The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras su(p, q) of the Cartan series Al and the pseudo-unitary algebras u(p, q), are completely determined and classified for arbitrary p, q. In addition to the su(p, q) and u(p, q) algebras, whose second cohomology group is well known to be trivi...

We prove a general theorem for constructing integral quantum cluster algebras over Z[q±1/2], namely, that under mild conditions the forms of nilpotent always possess algebra structures. These are then shown to be isomorphic corresponding upper algebras, again defined Z[q±1/2]. Previously, this was only known acyclic algebras. The is applied that, every symmetrizable Kac–Moody g and Weyl group e...