abstract This is an extension of quantum spinor construction in [DF2]. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, construct quantum spinor representations of U q (ˆ gl(n)) and explain classical and quantum boson-fermion correspondence. I. Introduction. The independent discovery of a q-deformation of universal enveloping algebra o...

In this paper, we introduce  the notions of   interval-valued and $(in,ivq)$-interval-valued fuzzy ($p$-,$q$- and $a$-) ideals    of   BCI algebras   and investigate some of their properties.   We then derive characterization theorems for these generalized interval-valued fuzzy ideals  and discuss their relationship.

A complete choice of generators of the center of the enveloping algebras of real quasi-simple Lie algebras of orthogonal type, for arbitrary dimension, is obtained in a unified setting. The results simultaneously include the well known polynomial invariants of the pseudo-orthogonal algebras so(p, q), as well as the Casimirs for many non-simple algebras such as the inhomogeneous iso(p, q), the N...

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...

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 $(q_n)$...

Let G be a nite group of Lie type deened over some nite eld GF(q). Let k be a eld of positive characteristic p not dividing q. Hecke functors tie together the representation theory of kG and that of Hecke algebras associated with nite reeection groups. In DDu1] the theory of vertices and sources for such algebras was introduced in the case of Hecke algebras H of type A, (that is Hecke algebras ...

In this paper, we deal with soft lattice implication algebras based on fuzzy sets. Using the concepts of fuzzy (implicative) filters, (∈,∈∨q)fuzzy (implicative) filters and (∈,∈∨q)-fuzzy (implicative) filters, some characterizations for ∈-soft sets and q-soft sets to be (implicative) filteristic soft lattice implication algebras are established.

where 1 denotes the universal relation on the base set. These Q-operations have a geometrical origin, but in [Jónsson 1991] Jónsson discusses them only in a context where he compares the expressive power of various clones of operations on binary relations. For instance, the operation defined in the picture above does not belong to the Tarski clone; that is, Q cannot be defined by using the bool...

Generalizing recent work of Brundan and Kleshchev, we introduce grading on Dipper-James’ q-Schur algebra, and prove a graded analogue of the Leclerc and Thibon’s conjecture on the decomposition numbers of the q-Schur algebra.