Related papers: Sylvester rank functions for amenable normal exten…

Given an action of a monoid $T$ on a ring $A$ by ring endomorphisms, and an Ore subset $S$ of $T$, a general construction of a fractional skew monoid ring $S^{\rm op} * A * T$ is given, extending the usual constructions of skew group rings…

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is…

Let k be a field of positive characteristic p and let G be a finite group. In this paper we study the category TsG of finitely generated commutative k-algebras A on which G acts by algebra automorphisms with surjective trace. If A = k[X],…

We say that a unital C*-algrebra A has the approximate positive factorization property (APFP) if every element of A is a norm limit of products of positive elements of A. (There is also a definition for the nonunital case.) T. Quinn has…

With any even Hecke symmetry R (that is a Hecke type solution of the Yang-Baxter equation) we associate a quasitensor category. We formulate a condition on R implying that the constructed category is rigid and its commutativity isomorphisms…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…

In 2022, using methods from ergodic theory, Kra, Moreira, Richter, and Robertson resolved a longstanding conjecture of Erd\H{o}s about sumsets in large subsets of the natural numbers. In this paper, we extend this result to several…

We prove that the crossed product Banach algebra $\ell^1(G,A;\alpha)$ that is associated with a ${\mathrm C}^\ast$-dynamical system $(A,G,\alpha)$ is amenable if $G$ is a discrete amenable group and $A$ is a strongly amenable ${\mathrm…

The main purpose of this paper is to introduce the random tensor with normal distribution, which promotes the matrix normal distribution to a higher order case. Some basic knowledge on tensors are introduced before we focus on the random…

We study amenability of definable and topological groups. Among our main technical tools is an elaboration on and strengthening of the Massicot-Wagner version of the stabilizer theorem, and some results around measures. As an application we…

We give a simple and unified proof showing that the unrestricted wreath product of a weakly sofic, sofic, linear sofic, or hyperlinear group by an amenable group is weakly sofic, sofic, linear sofic, or hyperlinear, respectively. By means…

Let G be a finite group and let F be a field of characteristic zero. In this paper we construct a generic G-crossed product over F using generic graded matrices. The center of this generic G-crossed product, denoted by F(G), is then the…

We show that the unrestricted wreath product of a sofic group by an amenable group is sofic. We use this result to present an alternative proof of the known fact that any group extension with sofic kernel and amenable quotient is again a…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…

We investigate the notion of relatively amenable topological action and show that the action of Thompson's group $T$ on $S^1$ is relatively amenable with respect to Thompson's group $F$. We use this to conclude that $F$ is exact if and only…

Let $A$ be an abelian variety over a global field $K$ of characteristic $p \ge 0$. If $A$ has nontrivial (resp. full) $K$-rational $l$-torsion for a prime $l \neq p$, we exploit the fppf cohomological interpretation of the $l$-Selmer group…

For two ideals $I$ and $J$ of a noetherian ring, we characterize, in terms of the vanishing of Tor modules, when the associated graded ring of the sum $I+J$ is isomorphic to the tensor product of the associated graded ring of $I$ and the…

The main aim of this paper is to prove $R$-triviality for simple, simply connected algebraic groups with Tits index $E_{8,2}^{78}$ or $E_{7,1}^{78}$, defined over a field $k$ of arbitrary characteristic. Let $G$ be such a group. We prove…

We introduce a general class of automorphisms of rotation algebras, the noncommutative Furstenberg transformations. We prove that fully irrational noncommutative Furstenberg transformations have the tracial Rokhlin property, which is a…

We prove that every unital stably finite simple amenable $C^*$-algebra $A$ with finite nuclear dimension and with UCT such that every trace is quasi-diagonal has the property that $A\otimes Q$ has generalized tracial rank at most one, where…