Related papers: Weights on bimodules
In this paper we investigate properties of the family of weight functions and especiallyin the "weight function" model. We etablish in theintroduced algebra topological sharp structures analogous tothe ones introduced in Colombeau algebra.
The work is devoted to the variety of $2$-dimensional algebras over an algebraically closed field. Firstly, we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of principal algebra series in the…
In this paper we address the problem of classification of simple weight modules over weak generalized Weyl algebras of rank one. The principal difference between weak generalized Weyl algebras and generalized weight algebras is that weak…
Weighted automata are a generalization of nondeterministic automata that associate a weight drawn from a semiring $K$ with every transition and every state. Their behaviours can be formalized either as weighted language equivalence or…
We extend the classical links between valuations and orderings on fields to Tignol-Wadsworth gauges and positive cones on finite-dimensional simple algebras with involution. We also study the compatibility of gauges and positive cones, and…
A modular grid is a pair of sequences $(f_m)_m$ and $(g_n)_n$ of weakly holomorphic modular forms such that for almost all $m$ and $n$, the coefficient of $q^n$ in $f_m$ is the negative of the coefficient of $q^m$ in $g_n$. Zagier proved…
We introduce and study bimeasurings from pairs of bialgebras to algebras. It is shown that the universal bimeasuring bialgebra construction, which arises from Sweedler's universal measuring coalgebra construction and generalizes the finite…
A general definition of a bimodule connection in noncommutative geometry has been recently proposed. For a given algebra this definition is compared with the ordinary definition of a connection on a left module over the associated…
We call a von Neumann algebra with finite dimensional center a multifactor. We introduce an invariant of bimodules over $\rm II_1$ multifactors that we call modular distortion, and use it to formulate two classification results. We first…
Let $\mathfrak g$ be a classical Lie superalgebra of type I or a Cartan-type Lie superalgebra {\bf W}$(n)$. We study weight $\mathfrak g$-modules using a method inspired by Mathieu's classification of the simple weight modules with finite…
We describe the notion of a \emph{weighting} along a submanifold $N\subset M$, and explore its differential-geometric implications. This includes a detailed discussion of weighted normal bundles, weighted deformation spaces, and weighted…
We consider the functions in two variables on an arbitrary poset, for which the convolution operation is defined. We obtain the generalization of incidence algebra and describe its properties: invertibility, the Jackobson radical,…
In this paper we propose an algebraic formalization of connectors in the quantitative setting, in order to address their non-functional features in architectures of component-based systems. We firstly present a weighted Algebra of…
We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach…
Let $\mathfrak{g}$ be a finite-dimensional simple complex Lie algebra. A layer sum is introduced as the sum of formal exponentials of the distinct weights appearing in an irreducible $\mathfrak{g}$-module. It is argued that the character of…
We study weight modules of the Lie algebra $W_2$ of vector fields on ${\mathbb C}^2$. A classification of all simple weight modules of $W_2$ with a uniformly bounded set of weight multiplicities is provided. To achieve this classification…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
We investigate weighted Lebesgue space estimates for the Bergman projection on a simply connected planar domain via the domain's Riemann map. We extend the bounds which follow from a standard change-of-variable argument in two ways. First,…
In this paper, we generalise part of the theory of hereditary algebras to the context of prospecies of algebras. Here, a prospecies is a generalisation of Gabriel's concept of species gluing algebras via projective bimodules along a quiver…
A universal weight function for a quantum affine algebra is a family of functions with values in a quotient of its Borel subalgebra, satisfying certain coalgebraic properties. In representations of the quantum affine algebra it gives…