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We prove a natural generalization of Szep's conjecture. Given an almost simple group $G$ with socle not isomorphic to an orthogonal group having Witt defect zero, we classify all possible group elements $x,y\in G\setminus\{1\}$ with $G={\bf…
Generalized Bott manifolds (over $\mathbb C$ and $\mathbb R$) have been defined by Choi, Masuda and Suh. In this article we extend the results of arXiv:1609.05630 on the topology of real Bott manifolds to generalized real Bott manifolds. We…
We derive an implicit description of the image of a semialgebraic set under a birational map, provided that the denominators of the map are positive on the set. For statistical models which are globally rationally identifiable, this yields…
Using the theory of $(\varphi, \Gamma)$-modules we generalizes Greenberg's construction of the $\Cal L$-invariant to semistable representations
We show that the basic categorical concept of an S-algebra as derived from the theory of Segal's Gamma-sets provides a unifying description of several constructions attempting to model an algebraic geometry over the absolute point. It…
The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further…
The idea that the cohomology of finite groups might be fruitfully approached via the cohomology of ambient semisimple algebraic groups was first shown to be viable in the papers [CPS75] and [CPSvdK77]. The second paper introduced, through a…
Dimitrov and Fioresi introduced an object that they call a generalized root system. This is a finite set of vectors in a euclidean space satisfying certain compatibilities between angles and sums and differences of elements. They conjecture…
When does Borel's theorem on free subgroups of semisimple groups generalize to other groups? We initiate a systematic study of this question and find positive and negative answers for it. In particular, we fully classify fundamental groups…
We study the set of circuits of a homogeneous ideal and that of its truncations, and introduce the notion of generic circuits set. We show how this is a well-defined invariant that can be used, in the case of initial ideals with respect to…
For semisimple Lie algebras, the BGG resolution is often viewed as a categorification of the Weyl character formula. For general linear Lie superalgebras, Brundan--Stroppel constructed an infinite resolution of the so-called Kostant simple…
Descriptive set theory was originally developed on Polish spaces. It was later extended to $\omega$-continuous domains [Selivanov 2004] and recently to quasi-Polish spaces [de Brecht 2013]. All these spaces are countably-based. Extending…
Given a graph $G$ whose edges are labeled by ideals of a commutative ring $R$ with identity, a generalized spline is a vertex labeling of $G$ by the elements of $R$ so that the difference of labels on adjacent vertices is an element of the…
We present a system of axioms motivated by a topological intuition: The set of subsets of any set is a topology on that set. On the one hand, this system is a common weakening of Zermelo-Fraenkel set theory ZF, the positive set theory GPK…
Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…
One can develop the basic structure theory of linear algebraic groups (the root system, Bruhat decomposition, etc.) in a way that bypasses several major steps in the standard development, including the self-normalizing property of Borel…
By a theorem of Chevalley the image of a morphism of varieties is a constructible set. The algebraic version of this fact is usually stated as a result on "extension of specializations" or "lifting of prime ideals". We present a difference…
The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…
In this paper we prove that if there is a Borel-cover gamma-set of cardinality the continuum, then there is one which is not hereditary. A set of reals X is a Borel-cover gamma-set iff for every countable family of Borel sets which is an…
Recently, the Elementary Process Theory (EPT) has been developed as a set of fundamental principles that might underlie a gravitational repulsion of matter and antimatter. This paper presents set matrix theory (SMT) as the foundation of the…