Constructions of quaternion and octonion algebras, suggested to have new level and sublevel values, are proposed and justified. In particular, octonion algebras of level and sublevel 6 and 7 are constructed. In addition, Hoffmann’s proof of the existence of infinitely many new values for the level of a quaternion algebra is generalised and adapted.

In this paper we begin a classification of simple and semisimple totally antiflexible algebras (finite-dimensional) over splitting fields of char. ^2, 3.. For such an algebra A , let P be the largest associative ideal in A and let /V+ be the radical of P. We determine all simple and semisimple totally antiflexible algebras in which N ■ N =0. Defining A to be of type (m, n) if N is nilpotent of ...

Let V be a vertex operator algebra. We construct a sequence of associative algebras A n (V) (n = 0; 1; 2; :::) such that A n (V) is a quotient of A n+1 (V) and a pair of functors between the category of A n (V)-modules which are not A n?1 (V)-modules and the category of admissible V-modules. These functors exhibit a bijection between the simple modules in each category. We also show that V is r...

In this paper we investigate the validity of a cancellation law for some classes of monounary algebras.

In this paper, we determine the isomorphism classes of the central simple Poisson algebras introduced earlier by the second author. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.

We describe a general framework to define dendriform algebras and a general construction to obtain new dendriform algebra structures from known structures and from linear operators. The construction includes recent constructions of the quadri-algebra, the ennea-algebras, the dendriformNijenhuis algebras and the octo-algebras.

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  Ulrich Hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...

The flux reconstruction (FR) methodology has proved to be an attractive approach to obtaining high-order solutions to hyperbolic partial differential equations. However, the utilization of somewhat arbitrarily defined correction polynomials in the application of these schemes, while adding some flexibility, detracts from their ease of implementation and computational efficiency. This paper desc...