Related papers: Recursively free reflection arrangements

Let $N/F$ be an odd degree Galois extension of number fields with Galois group $G$ and rings of integers ${\mathfrak O}_N$ and ${\mathfrak O}_F=\bo$ respectively. Let $\mathcal{A}$ be the unique fractional ${\mathfrak O}_N$-ideal with…

We show that every free amalgamation class of finite structures with relations and (symmetric) partial functions is a Ramsey class when enriched by a free linear ordering of vertices. This is a common strengthening of the…

Given a set $F$ of words, one associates to each word $w$ in $F$ an undirected graph, called its extension graph, and which describes the possible extensions of $w$ on the left and on the right. We investigate the family of sets of words…

We define a generalization $\mathfrak{G}$ of the Grassmann algebra $G$ which is well-behaved over arbitrary commutative rings $C$, even when $2$ is not invertible. In particular, this enables us to define a notion of superalgebras that does…

Let G be a simple algebraic group defined over an algebraically closed field k of characteristic p>0. Here we classify all irreducible kG-modules for which the principal A1 has no repeated composition factors, extending the work of…

We prove new separability results about free groups. Namely, if $H_1, \ldots , H_k$ are infinite index, finitely generated subgroups of a non-abelian free group $F$, then there exists a homomorphism onto some alternating group $f:F…

Let $\mathcal{W}(b)$ be a class of free Lie conformal algebras of rank $2$ with $\mathbb{C}[\partial]$-basis ${L,H}$ and relations \begin{eqnarray*} [L_\lambda L]=(\partial+2\lambda)L,\ \ [L_\lambda H]=\big(\partial+(1-b)\lambda\big)H, \ \…

Let $\mathcal{A}$ be a (not necessarily rational) conformal net. We show that the braided $\mathrm{W}^*$-tensor category $\text{Rep}(\mathcal{A})$ of representations of $\mathcal{A}$ is canonically a balanced $\mathrm{W}^*$-tensor category.…

In this article we explore a non-abelian torsion theory in the category of preordered groups: the objects of its torsion-free subcategory are the partially ordered groups, whereas the objects of the torsion subcategory are groups (with the…

A referee found an error in the proof of the Theorem 2 that we could not fix. More precisely, the proof of Lemma 2.1 is incorrect. Hence the fact that integer cohomology of complement of toric Weyl arrangements is torsion free is still a…

Finite covers are a technique for building new structures from simpler ones. The original motivation to study finite covers is in the Ladder theorem of Zilber which describes how totally categorical structures are built from strictly…

We prove that the property of a free group endomorphism being irreducible is a group invariant of the ascending HNN extension it defines. This answers a question posed by Dowdall-Kapovich-Leininger. We further prove that being irreducible…

A class of algebras is constructed using free fermions and the invariant antisymmetric tensors associated with irreducible holonomy groups. (This version contains minor typographical corrections and some additional references. )

We study fibers of word maps in finite, profinite, and residually finite groups. Our main result is that, for any word w in the free group on d generators, there exists $\epsilon > 0$ such that if G is a residually finite group with…

In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type $A_1$ by taking tensor products of a finite number of irreducible modules $M(\lambda, \alpha, \beta, \gamma)$ with irreducible highest weight…

This paper is the detailed version of math.QA/0403477 (T. Arakawa, Quantized Reductions and Irreducible Representations of W-Algebras) with extended results; We study the representation theory of the W-algebra $W_k(g)$ associated with a…

We study non-selfadjoint operator algebras that can be entirely understood via their finite-dimensional representations. In contrast with the elementary matricial description of finite-dimensional $\mathrm{C}^*$-algebras, in the…

We study some aspects of reflexive modules. For example, we search conditions for which reflexive modules are free or being very close to free modules.

In this paper, we show how to compute using Fitting ideals the nonfree locus of the moduli space of arrangements of a rank $3$ simple matroid, i.e., the subset of all points of the moduli space which parametrize nonfree arrangements. Our…

Consider the reduced free product of C*-algebras, (A,\phi)=(A_1,\phi_1)*(A_2,\phi_2), with respect to states \phi_1 and \phi_2 that are faithful. If \phi_1 and \phi_2 are traces, if the so-called Avitzour conditions are satisfied, (i.e. A_1…