Related papers: Commuting contractive idempotents in measure algeb…
Idempotent states on a compact quantum group are shown to yield group-like projections in the multiplier algebra of the dual discrete quantum group. This allows to deduce that every idempotent state on a finite quantum group arises in a…
The local kinematic formulas on complex space forms induce the structure of a commutative algebra on the space $\mathrm{Curv}^{\mathrm{U}(n)*}$ of dual unitarily invariant curvature measures. Building on the recent results from integral…
We call an operator algebra A {\em reversible} if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the {\em symmetric operator…
We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…
Commability is the finest equivalence relation between locally compact groups such that $G$ and $H$ are equivalent whenever there is a continuous proper homomorphism $G \to H$ with cocompact image. Answering a question of Cornulier, we show…
We call an algebra $A$ commutator-simple if $[A,A]$ does not contain nonzero ideals of $A$. After providing several examples, we show that in these algebras derivations are determined by a condition that is applicable to the study of local…
If $X$ is a locally compact space which admits commuting free and proper actions of locally compact groups $G$ and $H$, then the Brauer groups $\Br_H(G/X)$ and $\Br_G(X/H)$ are naturally isomorphic.
We define and investigate modulation invariant spaces on a locally compact abelian group $G$ with respect to a closed subgroup of the dual group $\widehat{G}$. Using a range function approach, we establish a characterization of modulation…
Meta-centralizers of non-locally compact group algebras are studied. Theorems about their representations with the help of families of generalized measures are proved. Isomorphisms of group algebras are investigated in relation with…
In this paper, the categorial property of compactness of an object, i. e. commuting of the corresponding $\Hom$ functor with coproducts, is studied in categories of $S$-acts and the corresponding structural properties of compact $S$-acts…
We establish two conditions equivalent to coamenability for type I locally compact quantum groups. The first condition is concerned with the spectra of certain convolution operators on the space…
Analytic properties of right topological groups have been extensively studied in the compact admissible case (i.e when the group has a dense topological center). This was inspired by the existence of a Haar measure on such groups. In this…
We recently introduced the notion of an idempotent system. This linear algebraic object is motivated by the structure of an association scheme. There is a type of idempotent system, said to be symmetric. In the present paper we classify up…
We show that the mapping class group of a compact orientable surface with higher complexity has the following extreme rigidity in the sense of measure equivalence: if the mapping class group is measure equivalent to a discrete group, then…
This paper is a review of concepts from graded commutative algebra with specific attention given to length and multiplicity. The author's motivation for this paper comes from the study of equivariant cohomology in algebraic topology where…
We study directed weighted graphs which are invariant under a nilpotent and cocompact group action. In particular, we consider the conic section K of the set of positive harmonic functions. We characterise the set of extreme points of the…
This paper, we consider some properties of rings via q-potent and periodic elements. In this paper we give some results of rings in which every element is a sum of an idempotent and a q-potent that commute; periodic rings and k-potent…
This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications.
Let $A$ be a unital, simple and Z-stable C$^*$-algebra. We show that the set of positive elements in $A$ (resp. $A \otimes K$) belonging to a fixed non-compact Cuntz class is contractible as a topological subspace of $A$ (resp. $A \otimes…
We consider endomorphism actions of arbitrary discrete semigroups on a connected metrizable topological group G. We give necessary and sufficient conditions for expansiveness of such actions when G is a Lie group or a compact…