Related papers: Quantifier Elimination and Rectilinearisation Theo…
We study the arithmetic property which allows to sharpen number-theoretic estimates. Previous results on this property are, as a rule, quantitive. The application of our general qualitive theorems to generalized hypergeometric functions…
We introduce and study a relative cancellation property for associative algebras. We also prove a characterization result for polynomial rings which partially answers a question of Kraft.
Real analytic generalized functions are investigated as well as the analytic singular support and analytic wave front of a generalized function in $\mathcal{G}(\Omega)$ are introduced and described.
We generalise a classic result of Rees to characterise analytically unramified local rings using Rees algebras of modules.
We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
Let $K$ be an algebraically closed field of characteristic different from $2$. We provide a positive solution to the Bahturin--Regev conjecture in the general finite-dimensional (non-graded) setting, assuming that $\operatorname{char}(K)$…
We propose and discuss how basic notions (quadratic modules, positive elements, semialgebraic sets, Archimedean orderings) and results (Positivstellensaetze) from real algebraic geometry can be generalized to noncommutative $*$-algebras. A…
Real algebraic geometry is the study of semi-algebraic sets, subsets of $\R^k$ defined by Boolean combinations of polynomial equalities and inequalities. The focus of this thesis is to study quantitative results in real algebraic geometry,…
This paper contains a complete proof of a fundamental theorem on the normalizers of unipotent subgroups in semisimple algebraic groups.
Let ${\mathcal C}$ be a fixed equisingularity class of irreducible germs of complex analytic plane curves. We compute a basis of the ${\mathbb C}[[x]]$-module of K\"ahler differentials for generic $\Gamma \in {\mathcal C}$, algorithmically,…
We generalize the framework of virtual substitution for real quantifier elimination to arbitrary but bounded degrees. We make explicit the representation of test points in elimination sets using roots of parametric univariate polynomials…
Work of Eagle, Farah, Goldbring, Kirchberg, and Vignati shows that the only separable C*-algebras that admit quantifier elimination in continuous logic are $\mathbb{C},$ $\mathbb{C}^2,$ $M_2(\mathbb{C}),$ and the continuous functions on the…
With a nilpotent element in a semisimple Lie algebra g one associates a finitely generated associative algebra W called a W-algebra of finite type. This algebra is obtained from the universal enveloping algebra U(g) by a certain Hamiltonian…
The paper gives the sufficient condition formulated in the syntactical form for all codescent morphisms of a variety of universal algebras satisfying the amalgamation property to be effective. This result is further used in proving that all…
We consider positive semidefinite kernels valued in the $*$-algebra of adjointable operators on a VE-space (Vector Euclidean space) and that are invariant under actions of $*$-semigroups. A rather general dilation theorem is stated and…
The cylindrical algebraic covering method was originally proposed to decide the satisfiability of a set of non-linear real arithmetic constraints. We reformulate and extend the cylindrical algebraic covering method to allow for checking the…
General linear electrodynamics allow for an arbitrary linear constitutive relation between the field strength two-form and induction two-form density if crucial hyperbolicity and energy conditions are satisfied, which render the theory…
For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…