Related papers: Quantifier Elimination and Rectilinearisation Theo…
We characterise algebras commutative with respect to a Yang-Baxter operator (quasi-commutative algebras) in terms of certain cosimplicial complexes. In some cases this characterisation allows the classification of all possible…
We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…
We provide a simple proof of the radial symmetry of any nonnegative minimizer for a general class of quasi-linear minimization problems
In this paper, we generalize an elementary real-analysis result to a class of topological vector spaces. We also give an example of a topological vector space to which the result cannot be generalized.
In this paper we consider the problem of quantizing theories defined over configuration spaces described by non-commuting parameters. If one tries to do that by generalizing the path-integral formalism, the first problem one has to deal…
Let g be a Lie bialgebra and let V be a finite-dimensional g-module. We study deformations of the symmetric algebra of V which are equivariant with respect to an action of the quantized enveloping algebra of g. In particular we investigate…
Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…
We give a novel and effective criterion for algebraicity of rational normal analytic surfaces constructed from resolving the singularity of an irreducible curve-germ on $CP^2$ and contracting the strict transform of a given line and all but…
We generalize in two steps the quantized action of the modular group on $q$-deformed real numbers introduced by Morier-Genoud and Ovsienko. First, we let the projective general linear group $PGL_2(\mathbb{Z})$ act on $q$-real numbers via a…
It is proved that classifiable simple separable nuclear purely infinite C*-algebras having finitely generated K-theory and torsion-free K_1 are semiprojective. This is accomplished by exhibiting these algebras as C*-algebras of infinite…
Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…
We review the definition of geometric quantization, which begins with defining a mathematical framework for the algebra of observables that holds equally well for classical and quantum mechanics. We then discuss prequantization, and go into…
We extend the notion of the quantization of the coefficients of the ordinary cluster algebras to the generalized cluster algebras by Chekhov and Shapiro. In parallel to the ordinary case, it is tightly integrated with certain…
This article explores the structure theory of compatible generalized derivations of finite-dimensional $\omega$-Lie algebras over a field $\mathbb{K}$. We prove that any compatible quasiderivation of an $\omega$-Lie algebra can be embedded…
A classical tool in the study of real closed fields are the fields $K((G))$ of generalised power series (i.e., formal sums with well-ordered support) with coefficients in a field $K$ of characteristic 0 and exponents in an ordered abelian…
We prove the existence of a strict deformation quantization for the canonical Poisson structure on the dual of an integrable Lie algebroid. It follows that any Lie groupoid C*-algebra may be regarded as a result of a quantization procedure.…
The goal of this article is to study some basic algebraic and combinatorial properties of "generalized $n$-series" over a commutative ring $R$, which are functions $s: \mathbf{Z}_{\geq 0} \to R$ satisfying a mild condition. A special…
The concept of quantization consists in replacing commutative quantities by noncommutative ones. In mathematical language an algebra of continuous functions on a locally compact topological space is replaced with a noncommutative…
A notion of generalized quantifier in computational complexity theory is explored and used to give a unified treatment of leaf language definability, oracle separations, type 2 operators, and circuits with monoidal gates. Relations to…