Related papers: Iterated Extensions and Uniserial Length Categorie…

In this article we extend the notion of determinantal representation of hypersurfaces to the determinantal representation of sections of the determinant line bundle of a vector bundle. We give several examples, and prove some necessary…

The separability tensor element of a separable extension of noncommutative rings is an idempotent when viewed in the correct endomorphism ring; so one speaks of a separability idempotent, as one usually does for separable algebras. It is…

We show that a braided monoidal category C can be endowed with the structure of a right (and left) module category over C \times C. In fact, there is a family of such module category structures, and they are mutually isomorphic if and only…

We study the classification of submodules of module categories over monoidal categories, extending ideas of Coulembier on the classification of tensor ideals in monoidal categories. We develop a framework that applies to module categories…

We study tensor categories that interpolate the representation categories of finite classical groups. There are (at least) two ways to approach these categories: via ultraproducts and via oligomorphic groups. Both have strengths and…

Let F be a non-Archimedean locally compact field of residue characteristic p, let D be a finite dimensional central division F-algebra and let R be an algebraically closed field of characteristic different from p. To any irreducible smooth…

For more than hundred years, various concepts were developed to understand the fields of geometric objects and invariant differential operators between them for conformal Riemannian and projective geometries. More recently, several general…

We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…

For any length category, we establish a set of rules (necessary and sufficient) that ensure a partial order on the isomorphism classes of simple objects such that the category is equivalent to the category of finite dimensional…

We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…

We introduce the notion of iterated group extensions, which, roughly speaking, is what one obtains by forming a group extension of a group extension. We interpret iterated extensions in terms of group cohomology, in the same way as…

We propose a theory of degenerations for derived module categories, analogous to degenerations in module varieties for module categories. In particular we define two types of degenerations, one algebraic and the other geometric. We show…

The first-order theory of finite and infinite trees has been studied since the eighties, especially by the logic programming community. Following Djelloul, Dao and Fr\"uhwirth, we consider an extension of this theory with an additional…

This article deals with universal deformations of dihedral representations with a particular focus on the question when the universal deformation is dihedral. Results are obtained in three settings: (1) representation theory, (2) algebraic…

In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into…

We give a new short proof that the wheeled operad of unimodular Lie algebras is Koszul and use this to explicitly construct its minimal resolution. A representation of this resolution in a finite dimensional vector space V we call a…

This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module $E$ over a DG category we define four deformation functors $\Def ^{\h}(E)$,…

We introduce a canonical isomorphism from the space of pure-type complex differential forms on a compact complex manifold to the one on its infinitesimal deformations. By use of this map, we generalize an extension formula in a recent work…

The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that…

This paper studies abelian categories that can be decomposed into smaller abelian categories via iterated recollements - such a decomposition we call a stratification. Examples include the categories of (equivariant) perverse sheaves and…