Related papers: Interval MV-algebras and generalizations

One of the key problems in dealing with color in rendering, shading, compositing, or image manipulation is that we do not have algebraic structures that support operations over colors. In this paper, we present an all-encompassing framework…

The famous Minkowski inequality provides a sharp lower bound for the mixed volume $V(K,M[n-1])$ of two convex bodies $K,M\subset\mathbb{R}^n$ in terms of powers of the volumes of the individual bodies $K$ and $M$. The special case where $K$…

We prove that Killing horizons in massive IIA supergravity preserve an even number of supersymmetries, and that their symmetry algebra contains an $\mathfrak{sl}(2, R)$ subalgebra, confirming the conjecture of [5]. We also prove a new class…

For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary…

In this paper, once recalled some properties of CMV-algebras, we introduce an expansion of the one-variable fragment of Lukasiewicz propositional logic whose algebraic semantics is the variety of CMV-algebras.

We introduce the notion of clone algebra, intended to found a one-sorted, purely algebraic theory of clones. Clone algebras are defined by true identities and thus form a variety in the sense of universal algebra. The most natural clone…

In his monograph on Infinite Abelian Groups, I. Kaplansky raised three ``test problems" concerning their structure and multiplicity. As noted by Azoff, these problems make sense for any category admitting a direct sum operation. Here, we…

The complete structure of the Casimir ${\cal{W}\cal{A}}_{\it{N}}$ algebras are shown to exist in such a way that the Casimir ${\cal{W}\cal{A}}_{\it{N}}$ algebra is a kind of truncated type of $\cal{W}_{\infty}$ algebra both in the primary…

We clarify the notion of the DS --- generalized Drinfeld-Sokolov --- reduction approach to classical ${\cal W}$-algebras. We first strengthen an earlier theorem which showed that an $sl(2)$ embedding ${\cal S}\subset {\cal G}$ can be…

We consider a four-dimensional globally hyperbolic spacetime $(M,g)$ conformal to Minkowski spacetime, together with a massless, conformally coupled scalar field. Using a bulk-to-boundary correspondence, one can establish the existence of…

This work is concerned with Mishchenko-Fomenko subalgebras and their restrictions to the adjoint orbits in a finite-dimensional complex semisimple Lie algebra. In this setting, it is known that each Mishchenko-Fomenko subalgebra restricts…

We show that there are functions $f$ in the H\"older class $C^{ { \alpha }}[0,1]$, $1< { \alpha }<2$ such that $f|_{A}$ is not convex, nor concave for any $A { \subset } [0,1]$ with $ { \bar { dim }_M } A> { \alpha }-1$. Our earlier result…

Recently, there is growing interest in the use of relative homology algebra to develop invariants using interval covers and interval resolutions (i.e., right minimal approximations and resolutions relative to interval-decomposable modules)…

A notion of local algebras is introduced in the theory of causal fermion systems. Their properties are studied in the example of the regularized Dirac sea vacuum in Minkowski space. The commutation relations are worked out, and the…

We present a mathematical structure which unifies mathematical structures of general relativity and quantum mechanics. It consists of the noncommutative algebra of compactly supported, complex valued functions ${\mathcal A}$, with…

This is the first in a series of papers devoted to the theory of decomposition spaces, a general framework for incidence algebras and M\"obius inversion, where algebraic identities are realised by taking homotopy cardinality of equivalences…

In the study of certain noncommutative versions of Minkowski spacetime there is still a large ambiguity concerning the characterization of their symmetries. Adopting as our case study the kappaMinkowski noncommutative space-time, on which a…

We introduce a concept of approximately invertible elements in non-unital normed algebras which is, on one side, a natural generalization of invertibility when having approximate identities at hand, and, on the other side, it is a direct…

Let $m(G)$ be the infimum of the volumes of all open subgroups of a unimodular locally compact group $G$. Suppose integrable functions $\phi_1 , \phi_2 \colon G \to [0,1]$ satisfy $\| \phi_1 \| \leq \| \phi_2 \|$ and $\| \phi_1 \| + \|…

It is well-known that future timelike infinity ($i^+$) in four-dimensional Minkowski spacetime is conformal to the unit three-dimensional hyperboloid ($H^3$). We asymptotically expand massive fields with spin $0,1,2$ near $i^+$ and…