相关论文: Aut-stable subspaces of Grassmann algebras

We apply the supergeometric analogue of Artin's algebraicity criteria to prove algebraicity for four moduli problems in supergeometry: supercurves, super Riemann surfaces, stable supercurves, and stable super Riemann surfaces. The…

Regular and higher regular graded algebras (in simplest case satisfying Von Neumann regularity $\Theta_{1}\Theta_{2}\Theta_{1}=\Theta_{1}$ instead of anticommutativity) are introduced and their properties are studied. They are described in…

We introduce two algebras associated with a subshift over an arbitrary alphabet. One is unital and the other not necessarily. We focus on the unital case and describe a conjugacy between Ott-Tomforde-Willis subshifts in terms of a…

In a companion paper [On semiclassical orthogonal polynomials via polynomial mappings, J. Math. Anal. Appl. (2017)] we proved that the semiclassical class of orthogonal polynomials is stable under polynomial transformations. In this work we…

In this paper we begin to study the subalgebra lattice of a Leibniz algebra. In particular, we deal with Leibniz algebras whose subalgebra lattice is modular, upper semi-modular, lower semi-modular, distributive, or dually atomistic. The…

Artin-Schelter regular algebras can be thought of as noncommutative versions of commutative polynomial rings, modeled after the special homological properties polynomial rings have as graded rings. First defined by Artin and Schelter in…

The goal of this paper is to study when uniform Roe algebras have certain $C^*$-algebraic properties in terms of the underlying space: in particular, we study properties like having stable rank one or real rank zero that are thought of as…

We describe a family of rational affine surfaces S with huge groups of automorphisms in the following sense: the normal subgroup of Aut(S) generated by all its algebraic subgroups is not generated by any countable family of such subgroups,…

Let $P\to X$ be a ${\mathbb P}^1$-bundle over a variety $X$. The aim of this note is to understand all connected, algebraic groups $$ \operatorname{Aut}^\circ(P)\subset G\subset \operatorname{Bir}( X\times {\mathbb P}^1). $$ We get a quite…

A very first step to develop non-commutative algebraic geometry is the arithmetic of polynomials in non-commuting variables over a commutative field, that is, the study of elements in free associative algebras. This investigation is…

Various structural properties of the space of symmetry breaking boundary conditions that preserve an orbifold subalgebra are established. To each such boundary condition we associate its automorphism type. It is shown that correlation…

We present some new and recent algorithmic results concerning polynomial system solving over various rings. In particular, we present some of the best recent bounds on: (a) the complexity of calculating the complex dimension of an algebraic…

It is known that a matrix polynomial with unitary matrix coefficients has its eigenvalues in the annular region $\frac{1}{2} < |\lambda| < 2$. We prove in this short note that under certain assumptions, matrix polynomials with either doubly…

We can define the adjacency algebra of an association scheme over arbitrary field. It is not always semisimple over a field of positive characteristic. The structures of adjacency algebras over a field of positive characteristic have not…

We determine the invariants characterizing the $Sp(n)$-orbits in the real Grassmannian $Gr^\R(2k,4n)$ of the $2k$-dimensional complex and $\Sigma$-complex subspaces of a $4n$-dimensional Hermitian quaternionic vector space. A…

This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…

We show that the set of periods of an automorphism of the affine plane defined over a $p$-adic field is bounded above by a constant independent from the automorphism. We deduce from this result a new proof in arithmetic dynamics of the…

It is a widely open problem to determine which monomials in the n-variable polynomial ring $K[x_1,...,x_n]$ over a field $K$ have the Gotzmann property, i.e. induce a Borel-stable Gotzmann monomial ideal. Since 2007, only the case $n \le 3$…

We study the cohomology of Aut(F_n) and Out(F_n) with coefficients in the modules \wedge^q H, \wedge H^*, Sym^q H or Sym^q H^*, where H is the Out(F_n)-module obtained by abelianising the free group F_n. For reasons which are not…

We first study situations where the stable AF-algebras defined by two square primitive nonsingular incidence matrices with nonnegative integer matrix elements are isomorphic even though no powers of the associated automorphisms of the…