Related papers: Sums of two square-zero selfadjoint or skew-selfad…

Let $G$ be a group. The directed endomorphism graph, $\dend(G)$ of $G$ is a directed graph with vertex set $G$ and there is a directed edge from the vertex $a$ to the vertex $b$ if $a \neq b$ and there exists an endomorphism on $G$ mapping…

It is shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism. The geometric structure of the variety is described by methods of equivariant lifting and…

Let S and R be the rings of regular functions on affine algebraic varieties over a field of characteristic 0, R be embedded as a subring in S, and F : S --> S be an endomorphism such that F(R) subset R. Suppose that every ideal of height 1…

Let $\F$ denote a field and let $V$ denote a vector space over $\F$ with finite positive dimension. Consider a pair $A,A^*$ of diagonalizable $\F$-linear maps on $V$, each of which acts on an eigenbasis for the other one in an irreducible…

Let G be a unitary group of a signed-Hermitian form h given over a non-Archimedian local field k of residue characteristic not two. Let V be the vector space on which h is defined. We consider minimal skew-strata, more precisely pairs (b,a)…

This work addresses some relevant characteristics and properties of $q$-generalized associative algebras and $q$-generalized dendriform algebras such as bimodules, matched pairs. We construct for the special case of $q=-1$ an…

Let $F$ be a field of odd characteristic, $E$ be a finite extension of $F$ equipped an involution with subfield of fixed points $E_0$ containing $F$ and $V$ be a finite dimensional $E$-vector space with a non-degenerate hermitian form $h$.…

We define the flag space and space of singular vectors for an arrangement A of hyperplanes in projective space equipped with a system of weights a: A --> C. We show that the contravariant bilinear form of the corresponding weighted central…

M-theory compactified on S^7/Z_k allows for a four-dimensional, asymptotically AdS cosmology. The holographic dual consists of ABJM theory with a non-supersymmetric marginal deformation. At weak 't Hooft coupling the dual theory possesses a…

Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. Let $End(V)$ denote the $K$-algebra consisting of all $K$-linear transformations from $V$ to $V$. We consider a pair $A,A^* \in End(V)$ that…

Let $\widehat{\mathbb{F}\mathbb{S}et}$ be the groupoid of finite sets and bijections between them equipped with the canonical symmetric rig category structure given by the disjoint union and the cartesian product of finite sets. We prove…

Let $\mathcal A:U\to V$ be a linear mapping between vector spaces $U$ and $V$ over a field or skew field $\mathbb F$ with symmetric, or skew-symmetric, or Hermitian forms $\mathcal B:U\times U\to\mathbb F$ and $\mathcal C:V\times…

Let $\Sigma=\{a_1, \ldots , a_n\}$ be a set of positive integers with $a_1 < \ldots < a_n$ such that all $2^n$ subset sums are pairwise distinct. A famous conjecture of Erd\H{o}s states that $a_n>C\cdot 2^n$ for some constant $C$, while the…

Endomorphisms of Weyl algebras are studied using bimodules. Initially, for a Weyl algebra over a field of characteristic zero, Bernstein's inequality implies that holonomic bimodules finitely generated from the right or left form a monoidal…

The two main theorems proved here are as follows: If $A$ is a finite dimensional algebra over an algebraically closed field, the identity component of the algebraic group of outer automorphisms of $A$ is invariant under derived equivalence.…

We study real bihomogeneous polynomials $r(z,\bar{z})$ in $n$ complex variables for which $r(z,\bar{z}) \|z\|^2$ is the squared norm of a holomorphic polynomial mapping. Such polynomials are the focus of the Sum of Squares Conjecture, which…

Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in terms of systems of quadratic forms, is obtained. A refined…

It is well-known that gauging a finite 0-form symmetry in a quantum field theory leads to a dual symmetry generated by topological Wilson line defects. These are described by the representations of the 0-form symmetry group which form a…

Let $V$ be a two-dimensional vector space over a field $\mathbb F$ of characteristic not $2$ or $3$. We show there is a canonical surjection $\nu$ from the set of suitably generic commutative algebra structures on $V$ modulo the action of…

We generalize the Abel--Hurwitz identities to an almost entirely noncommutative setting. Namely, let $V$ be a finite set of size $n$, and let $\mathbb{L}$ be any noncommutative ring. For each $s\in V$, let $x_{s}\in\mathbb{L}$. Set $x\left(…