In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...

In a recent work [FR], Frenkel and Reshetikhin developed the theory of q-vertex operators. They showed that n-point correlation functions associated to q-vertex operators satisfy a qdifference equation called q-deformed Kniznik-Zamolodchikov equation. In the derivation of this equation, a crucial point is that the quantum affine algebra is a quasi-triangular Hopf algebra. By using several prope...

Abstract. Let K be any unital commutative Q-algebra and z = (z1, z2, · · · , zn) commutative or noncommutative variables. Let t be a formal central parameter and K[[t]]〈〈z〉〉 the formal power series algebra of z over K[[t]]. In [Z6], for each automorphism Ft(z) = z−Ht(z) of K[[t]]〈〈z〉〉 with Ht=0(z) = 0 and o(H(z)) ≥ 1, a NCS (noncommutative symmetric) system ([Z5]) ΩFt has been constructed. Cons...

1.1. In [1] N. Reshetikhin and the second author introduced new Poisson algebras Wq(g), which are q–deformations of the classical W–algebras. The Poisson algebra Wq(g) is by definition the center of the quantized universal enveloping algebra Uq(ĝ) at the critical level, where g is the Langlands dual Lie algebra to g. It was shown in [1] that the Wakimoto realization of Uq(ĝ ) constructed in [2]...

We prove that given a bialgebra surjection π : E → H with nilpotent kernel such that H is a Hopf algebra which is formally smooth as a K-algebra, then π has a section which is a right H-colinear algebra homomorphism. Moreover, if H is also endowed with an ad-invariant integral, then the section can be chosen to be H-bicolinear. We also deal with the dual case. As an application, we prove that e...

This paper is concerned with the effective symbolic computation of operators under composition. Examples include differential operators under composition and vector fields under the Lie bracket. A basic fact about such operators is that, in general, they do not commute. A basic fact about applied mathematicians is that they often rewrite expressions involving noncommuting operators in terms of ...

Let B be a commutative algebra and A B-algebra (determined by an homomorphism ?:B?A). M. D. Staic introduced Hochschild like cohomology H•((A,B,?);A) called secondary cohomology, to describe the non-trivial deformations of A. J. Laubacher et al later obtained natural construction new chain complex C¯•(A,B,?) in process introducing cyclic (co)homology. In this paper, we establish connection betw...

We study Kuperberg invariants for sutured manifolds in the case of a semidirect product an involutory Hopf superalgebra $H$ with its automorphism group $\text{Aut}(H)$. These are topological balanced 3-manifolds endowed homomorphism fundamental into $\text{Aut}(H)$ and possibly $\text{Spin}^c$ structure homology orientation. show that these computed via form Fox calculus that, if is $\mathbb{N}...