Related papers: A note on fully commutative elements in complex re…

In this note we introduce and study basic properties of two types of modules over a commutative noetherian ring $R$ of positive prime characteristic. The first is the category of modules of finite $F$-type. These objects include reflexive…

Every mathematician is familiar with the beautiful structure of finite commutative groups. What is less well known is that finite commutative semigroups also have a neat and well-described structure. We prove this in an efficient fashion.…

Given a group $G$, we write $g^G$ for the conjugacy class of $G$ containing the element $g$. A theorem of B. H. Neumann states that if $G$ is a group in which all conjugacy classes are finite with bounded size, then the commutator subgroup…

Given an irreducible well-generated complex reflection group W with Coxeter number h, we call a Coxeter element any regular element (in the sense of Springer) of order h in W; this is a slight extension of the most common notion of Coxeter…

In our previous papers we introduced categorical invariants, which are, roughly speaking, sets of triangulated subcategories in a given triangulated category and their quotients. Here is extended the list of examples, where these sets are…

We generalize the well known characterizations of totally nonnegative and oscillatory matrices, due to F.R.Gantmacher, M.G.Krein, A.Whitney, C.Loewner, M.Gasca, and J.M.Pena to the case of an arbitrary complex semisimple Lie group.

In an earlier paper, we defined and studied q-analogues of the Stirling numbers of both types for the Coxeter group of type B. In the present work, we show how this approach can be extended to all irreducible complex reflection groups G.…

We define parabolic quasi-Coxeter elements in well generated complex reflection groups. We characterize them in multiple natural ways, and we study two combinatorial objects associated with them: the collections $\operatorname{Red}_W(g)$ of…

The star operation, originally introduced by Kazhdan and Lusztig, was later specialized by Ernst to the so-called weak star reduction on the set of fully commutative elements of a Coxeter group. In this paper, we classify the star and weak…

Let G be a finite group of exponent m and let k be a field of characteristic prime to m, containing the m-th roots of unity. For any Rost cycle module M over k, we construct exact sequences detecting the unramified elements in Serre's group…

Let $m,n$ be positive integers and $w$ a multilinear commutator word. Assume that $G$ is a finite group having subgroups $G_1,\ldots,G_m$ whose union contains all $w$-values in $G$. Assume further that all elements of the subgroups…

We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group $W$. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit basis of the…

The aim of this article is to extend the notions of strongly hollow and completely strongly hollow ideals of commutative rings to multiplicative lattices. We investigate their basic structural properties and prove several characterizations…

We prove that commutative semirings in a cartesian closed presentable $\infty$-category, as defined by Groth, Gepner, and Nikolaus, are equivalent to product-preserving functors from the $(2,1)$-category of bispans of finite sets. In other…

In this paper I consider all possible properties from commutative algebra for polynomial composites and monoid domains. The aim is full characterization of these structures. I start with the examination of group, ring, modules properties,…

This article records basic topological, as well as homological properties of the space of homomorphisms Hom(L,G) where L is a finitely generated discrete group, and G is a Lie group, possibly non-compact. If L is a free abelian group of…

We show that for the family of complex reflection groups $G=G(m,p,2)$ appearing in the Shephard--Todd classification, the endomorphism ring of the reduced hyperplane arrangement $A(G)$ is a non-commutative resolution for the coordinate ring…

In this article we consider a space B_{com}G assembled from commuting elements in a Lie group G first defined in [Adem, Cohen, Torres-Giese 2012]. We describe homotopy-theoretic properties of these spaces using homotopy colimits, and their…

Let $R$ be any associative ring with $1$, $n\ge 3$, and let $A,B$ be two-sided ideals of $R$. In the present paper we show that the mixed commutator subgroup $[E(n,R,A),E(n,R,B)]$ is generated as a group by the elements of the two following…

Let $G$ be a finite group. A coprime commutator in $G$ is any element that can be written as a commutator $[x,y]$ for suitable $x,y\in G$ such that $\pi(x)\cap\pi(y)=\emptyset$. Here $\pi(g)$ denotes the set of prime divisors of the order…