Related papers: An algebraic approach to weak and delay bismulatio…
A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented in block diagonal matrix form (resulting in the Wedderburn decomposition), a general form of polyadic…
Recently it has been shown that cumulants significantly simplify the analysis of multipartite weak measurements. Here we consider the mathematical structure that underlies this, and find that it can be formulated in terms of what we call…
For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…
We extend the weak Bruhat order of a finite Coxeter group to the set of its coclasses, modulo parabolic standard subgroups. We use this order to describe associative algebra structures on the vector spaces spanned by the faces of…
A deductive system is structurally complete if its admissible inference rules are derivable. For several important systems, like modal logic S5, failure of structural completeness is caused only by the underivability of passive rules, i.e.…
In this paper, we study weak bialgebras and weak Hopf algebras. These algebras form a class wider than bialgebras respectively Hopf algebras. The main results of this paper are Kaplansky's constructions type which lead to weak bialgebras or…
Recent works have shown that defining a behavioural equivalence that matches the observational properties of a quantum-capable, concurrent, non-deterministic system is a surprisingly difficult task. We explore coalgebras over distributions…
We review how an algebraic formulation for the dynamics of a physical system allows to describe a reduction procedure for both classical and quantum evolutions.
Let $\mathbb{K}$ be the set of hybrid numbers. This paper is to look for all the weak Hopf structures on $\mathbb{K}$. Once $\mathbb{K}$ is endowed with a structure of a weak Hopf algebra, we shall compute the source algebra and target…
In this paper, we introduce the concepts of representation and dual representation for averaging Leibniz algebras. We also develop a cohomology theory for these algebras. Additionally, we explore the infinitesimal and formal deformation…
We describe an equivalent formulation of algebraic weak factorisation systems, not involving monads and comonads, but involving double categories of morphisms equipped with a lifting operation satisfying lifting and factorisation axioms.
The aim of this paper is first to introduce and study Rota-Baxter cosystems and bisystems as generalization of Rota-Baxter coalgebras and bialgebras, respectively, with various examples. The second purpose is to provide an alternative…
We study twisted modules for (weak) quantum vertex algebras and we give a conceptual construction of (weak) quantum vertex algebras and their twisted modules. As an application we construct and classify irreducible twisted modules for a…
We show that first-order logic can be translated into a very simple and weak logic, and thus set theory can be formalized in this weak logic. This weak logical system is equivalent to the equational theory of Boolean algebras with three…
Delta lenses are functors equipped with a suitable choice of lifts, and are used to model bidirectional transformations between systems. In this paper, we construct an algebraic weak factorisation system whose R-algebras are delta lenses.…
We discuss the concepts of fine and coarse moduli spaces in the context of finite dimensional algebras over algebraically closed fields. In particular, our formulation of a moduli problem and its potential strong or weak solution is adapted…
We propose a definition of double categories whose composition of 1-cells is weak in both directions. Namely, a doubly weak double category is a double computad -- a structure with 2-cells of all possible double-categorical shapes --…
This paper introduces the counterpart of strong bisimilarity for labelled transition systems extended with time-out transitions. It supports this concept through a modal characterisation, congruence results for a standard process algebra…
The incidence algebra of a partially ordered set (poset) supports in a natural way also a coalgebra structure, so that it becomes a m-weak bialgebra even a m-weak Hopf algebra with M\"obius function as antipode. Here m-weak means that…
Let A be a finite dimensional unital associative algebra over a field K, which is also equipped with a coassociative counital coalgebra structure (\Delta,\eps). A is called a Weak Bialgebra if the coproduct \Delta is multiplicative. We do…