Related papers: On the relative Nullstellensatz in nonarchimedean …
Let $K$ be an algebraically closed field endowed with a complete non-archimedean norm with valuation ring $R$. Let $f\colon Y\to X$ be a map of $K$-affinoid varieties. In this paper we study the analytic structure of the image $f(Y)\subset…
We address the question of identifying non-smooth points in affine real algebraic varieties. A simple algebraic criterion will be formulated and proven. As an application we can answer several questions about the configuration spaces of…
Let G be a connected and simply connected real Lie group with Lie algebra g. Semialgebraic subsets of the unitary dual of G are defined and a strict Positivstellensatz for positive elements of the universal enveloping algebra of g is…
We prove that the notion of relative property (T) (or rigidity) for inclusions of finite von Neumann algebras defined in [Po1] is equivalent to a weaker property, in which no ``continuity constants'' are required. The proof is by…
The geometric form of Hilbert's Nullstellensatz may be understood as a property of "geometric saturation" in algebraically closed fields. We conceptualise this property in the language of first order logic, following previous approaches and…
For every non-exceptional affine Lie algebra, we explicitly construct a positive geometric crystal associated with a fundamental representation. We also show that its ultra-discretization is isomorphic to the limit of certain perfect…
In this paper a finite dimensional unital associative algebra is presented, and its group of algebra automorphisms is detailed. The studied algebra can physically be understood as the creation operator algebra in a formal quantum field…
Each relational structure X has an associated Gaifman graph, which endows X with the properties of a graph. Suppose that X is infinite, connected and of bounded degree. A first-order sentence in the language of X is almost surely true…
Let ${\mathcal N}$ and ${\mathcal M}$ be nests on Banach spaces $X$ and $Y$ over the (real or complex) field $\mathbb F$ and let $\mbox{\rm Alg}{\mathcal N}$ and $\mbox{\rm Alg}{\mathcal M}$ be the associated nest algebras, respectively. It…
In this paper it is shown that for locally trivial complex analytic morphisms between some reduced spaces the Relative Riemann-Hilbert Theorem still holds up to torsion, i.e. tame flat relative connections on torsion-free sheaves are in…
The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…
The theory of singularities defined by Frobenius has been extensively developed for $F$-finite rings and for rings that are essentially of finite type over excellent local rings. However, important classes of non-local excellent rings, such…
Using the Burklund-Schlank-Yuan abstraction of ``algebraically closed" to ``Nullstellensatzian", we show that a $G$-Tambara functor is Nullstellensatzian if and only if it is the coinduction of an algebraically closed field (for any finite…
The results in the paper are related to the classification problem for invariant subspaces of multiplication operators in several variables. The main results consist of characterizations, in the two dimensional case, of ideals of…
In this paper we develop a number of results and notions concerning Positivstellens\"atze for semirings (preprimes) of commutative unital real algebras. First we reduce the Archimedean Positivstellensatz for semirings to the corresponding…
Arbitrary representations of a commutative unital ($\ast$-) $\mathbb{F}$-algebra $A$ as a subalgeba of $\mathbb{F}^X$ are considered, where $\mathbb{F}=\mathbb{C}$ or $\mathbb{R}$ and $X\neq\emptyset$. The Gelfand spectrum of $A$ is…
We establish that the extended Robba rings associated to a perfect nonarchimedean field of characteristic p, which arise in p-adic Hodge theory as certain completed localizations of the ring of Witt vectors, are strongly noetherian Banach…
We give a geometric proof of inverse Hamiltonian reduction for all affine W-algebras in type A at generic level, a certain embedding of the affine W-algebra corresponding to an arbitrary nilpotent in $\mathfrak{gl}_N$ into that…
In this paper, we study nullity-2 toroidal extended affine Lie algebras in the context of vertex algebras and their $\phi$-coordinated modules. Among the main results, we introduce a variant of toroidal extended affine Lie algebras,…
The paper is devoted to the investigation of finite dimensional commutative nilpotent (associative) algebras N over an arbitrary base field of characteristic zero. Due to the lack of a general structure theory for algebras of this type (as…