Related papers: Relative unitary commutator calculus and applicati…
This article explains basic constructions and results on group algebras and their cohomology, starting from the point of view of commutative algebra. It provides the background necessary for a novice in this subject to begin reading Dave…
The survey is dedicated to a celebrated series of quantitave results, developed by the Lithuanian school of probability, on the normal approximation for a real-valued random variable. The key ingredient is a bound on cumulants of the type…
We extend work of the first author concering relative double commutants and approximate double commutants of unital subalgebras of unital C*-algebras, including metric versions involving distance estimates. We prove metric results for AH…
This article concerns a class of generalized linear mixed models for clustered data, where the random effects are mapped uniquely onto the grouping structure and are independent between groups. We derive necessary and sufficient conditions…
The modular commutator is a recently discovered multipartite entanglement measure that quantifies the chirality of the underlying many-body quantum state. In this Letter, we derive a universal expression for the modular commutator in…
This paper presents a significant advancement in the estimation of the Composite Link Model within a penalized likelihood framework, specifically designed to address indirect observations of grouped count data. While the model is effective…
We prove that amenability of a unitary co-representation $U$ of a locally compact quantum group passes to unitary co-representations that weakly contain $U$. This generalizes a result of Bekka, and answers affirmatively a question of…
We give a natural generalization of the classification of commutative rings of ordinary differential operators, given in works of Krichever, Mumford, Mulase, and determine commutative rings of operators in a completed ring of partial…
Let $R$ be a commutative ring. We investigate $R$-modules which can be written as \emph{finite} sums of {\it {second}} $R$-submodules (we call them \emph{second representable}). We provide sufficient conditions for an $R$-module $M$ to be…
The article is developing homological algebra in modules over non-unital rings and algebras. The main application is the definition and study of (directed) homology of $(\infty,1)$-categories and of directed spaces, including relative…
We calculate the cluster modular groups of affine and doubly extended typecluster algebras in a uniform way by introducing a new family of quivers. We use this uniformdescription to construct a natural finite quotient of the cluster complex…
We extend the Ax-Katz theorem for a single polynomial from finite fields to the rings Z_m with m composite. This extension not only yields the analogous result, but gives significantly higher divisibility bounds. We conjecture what computer…
Multiplier ideals, and the vanishing theorems they satisfy, have found many applications in recent years. In the global setting they have been used to study pluricanonical and other linear series on a projective variety. More recently, they…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
We adapt the commutator theory of universal algebra to the particular setting of racks and quandles, exploiting a Galois connection between congruences and certain normal subgroups of the displacement group. Congruence properties such as…
In the present paper we continue the study of the elementary commutator subgroups $[E(n,A),E(n,B)]$, where $A$ and $B$ are two-sided ideals of an associative ring $R$, $n\ge 3$. First, we refine and expand a number of the auxiliary results,…
In this paper, we propose a new conjecture describing the structure of the unitary dual in terms of Arthur representations for connected reductive algebraic groups defined over any non-Archimedean local field of characteristic zero. This…
Let $R$ be a finite ring and $r \in R$. The aim of this paper is to study the probability that the commutator of a randomly chosen pair of elements of $R$ equals $r$.
Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard-Stratonovich transformation. Here, we complete this extension by including arbitrary…
The theory of elliptic modular forms has gained significant momentum from the discovery of relaxed yet well-behaved notions of modularity, such as mock modular forms, higher order modular forms, and iterated Eichler-Shimura integrals.…