in the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup s with a weight function w into a proper h*-algebra a in terms of w-bounded continuous positive definite a-valued functions on s. a generalization of a well-known result of k. harzallah is obtained. an earlier conjecture of the author ...

By a Boolean inverse semigroup we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse semigroup S in a Boolean inverse semigroup which are tight in a certain well defined technical sense. These representations are supposed to preserve as much as possible any trace of Booleannes present in the semilattice of idempotents of ...

In [3] Bruns, Gubeladze, and Trung define the notion of polytopal semigroup ring as follows. Let P be a lattice polytope in R, i. e. a polytope whose vertices have integral coordinates, and K a field. Then one considers the embedding ι : R → R, ι(x) = (x, 1), and chooses SP to be the semigroup generated by the lattice points in ι(P ); the K-algebra K[SP ] is called a polytopal semigroup ring. S...

For each real number Λ a Lie algebra of nonlinear vector fields on three dimensional Euclidean space is reported. Although each algebra is mathematically isomorphic to gl(3, R), only the Λ = 0 vector fields correspond to the usual generators of the general linear group. The Λ < 0 vector fields integrate to a nonstandard action of the general linear group; the Λ > 0 case integrates to a local Li...

Introduction The purpose of this expository article is to describe in an elementary and homogeneous manner, the relationship between the geometric and algebraic multiplicities of isolated critical points of holomorphic functions. In particular , I am interested in the setting where the function is invariant under some group action. The emphasis is on functions invariant under actions of nite gr...

Abstract. The normal symmetric triality algebras (STA’s) and the normal Lie related triple algebras (LRTA’s) have been recently introduced by the second author, in connection with the principle of triality. It turns out that the unital normal LRTA’s are precisely the structurable algebras extensively studied by Allison. It will be shown that the normal STA’s (respectively LRTA’s) are the algebr...

On any set X may be defined the free algebra R〈X〉 (respectively, free commutative algebra R[X]) with coefficients in a ring R. It may also be equivalently described as the algebra of the free monoid X∗ (respectively, free commutative monoid M (X)). Furthermore, the algebra of differential polynomials R{X} with variables inX may be constructed. The main objective of this contribution is to provi...

We introduce the concept of a semigroup coupled cell network and show that the collection of semigroup network vector fields forms a Lie algebra. This implies that near a dynamical equilibrium the local normal form of a semigroup network is a semigroup network itself. Networks without the semigroup property will support normal forms with a more general network architecture, but these normal for...

In this paper we define the concepts of co-medial algebra and regular algebra and we will show that for a regular co-medial algebra (A, f , g), there exist a commutative semigroup (A,+), such that the operations f , g have the linear representation on (A,+). As a consequence of above result, we have the linear representation of an n−ary medial groupoid with an regular element, which was obtaine...

The non-commutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We obtain a distance formula to an arbitrary wotclosed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is us...