Under a perturbed triple product defined on three semisimple commutative Banach algebras with the influence of two homomorphisms them and that carry certain characteristics, we proved spectral extension property is stable.

This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras An(V ) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V ) is a semisimple associative algebra. 2000MSC:17B69

We evaluate the sum of a finite group of linear characters of a Hopf algebra, at all grouplike and skew-primitive elements, and mention results for products of skew-primitive elements. Examples include quantum groups associated to semisimple and abelian Lie algebras, and degenerate affine Hecke algebras of reductive type with trivial parameter.

The aim of this work is to study a class of non-archimedean valued measures on MV-algebras. We call them hyperreal states and their definition naturally arise from (the uniform version of) Di Nola representation theorem for MV-algebras (cf [5, 6]): for any MV-algebra A = (A,⊕,¬,>,⊥) there exists a ultrafilter U on the cardinality of A such that A embeds into (∗[0, 1]U) Spec(A) (where as usual S...

We classify all integrable triples in simple Lie algebras, up to equivalence. The importance of this problem stems from the fact that for each such equivalence class one can construct corresponding hierarchy bi-Hamiltonian PDE. simplest triple $(f,0,e)$ $\mathfrak{sl}_2$ corresponds KdV hierarchy, and $(f,0,e_\theta)$, where $f$ is sum negative root vectors $e_\theta$ highest vector a algebra, ...