相关论文: Coarse direct products and property {C}

We consider integrable category $\mathcal{O}$ representations of Borcherds--Kac--Moody algebras whose Cartan matrix is finite dimensional, and determine the necessary and sufficient conditions for which the tensor product of irreducible…

Let $X^{(2)}$ denote the second symmetric product space of a partially ordered vector space $X$, endowed with the projective cone. A characterization of linear maps $T\colon X^{(2)}\to X^{(2)}$ which preserve the set of all positive…

We give some properties of cosymplectic Lie algebras, we show, in particular, that they support a left symmetric product. We also give some constructions of cosymplectic Lie algebras, as well as a classification in three and…

Let $H$ and $K$ be two complex inner product spaces with dim$(X)\geq 2$. We prove that for each non-zero additive mapping $A:H \to K$ with dense image the following statements are equivalent: $(a)$ $A$ is (complex) linear or…

A classical tensor product $A \,\otimes\, B$ of complete lattices $A$ and $B$, consisting of all down-sets in $A \times B$ that are join-closed in either coordinate, is isomorphic to the complete lattice $Gal(A,B)$ of Galois maps from $A$…

We study the rich behavior of ergodicity and conservativity of Cartesian products of infinite measure preserving transformations. A class of transformations is constructed such that for any subset $R\subset \mathbb Q\cap (0,1)$ there exists…

We take a new look at dilation theory for nonself-adjoint operator algebras. Among the extremal (co)extensions of a representation, there is a special property of being fully extremal. This allows a refinement of some of the classical…

We prove the inequality $$ \as A\ast_CB\le\max\{\as A,\as B,\as C+1\} $$ and we apply this inequality to show that the asymptotic dimension of any right-angled Coxeter group does not exceed the dimension of its Davis' complex.

In this paper, we study properties of asymptotic resemblance relations induced by compatible coarse structures on groups. We generalize the notion of asymptotic dimensiongrad for groups with compatible coarse structures and show this notion…

Dualising the construction of a polyhedral product, we introduce the notion of a polyhedral coproduct as a certain homotopy limit over the face poset of a simplicial complex. We begin a study of the basic properties of polyhedral…

Consider an exact action of discrete group $G$ on a separable $C^*$-algebra $A$. It is shown that the reduced crossed product $A\rtimes_{\sigma, \lambda} G$ is strongly purely infinite - provided that the action of $G$ on any quotient $A/I$…

Let $X$ be the product of two projective spaces and consider the general CICY threefold $Y$ in $X$ with configuration matrix $A$. We prove the finiteness part of the analogue of the Clemens' conjecture for such a CICY in low bidegrees. More…

Let $X$ be an infinite compact metric space with finite covering dimension and let $\alpha, \beta : X\to X$ be two minimal homeomorphisms. We prove that the crossed product $C^*$-algebras $C(X)\rtimes_\alpha\Z$ and $C(X)\rtimes_\belta\Z$…

We introduce and study the continuous Rokhlin property for actions of compact groups on C*-algebras. An important technical result is a characterization of the continuous Rokhlin property in terms of asymptotic retracts. As a consequence,…

In this paper, we show that the strong embeddability has fibering permanence property and is preserved under the direct limit for the metric space. Moreover, we show the following result: let $G$ is a finitely generated group with a coarse…

We discuss the interplay between K-theoretical dynamics and the structure theory for certain C*-algebras arising from crossed products. For noncommutative C*-systems we present notions of minimality and topological transitivity in the…

In exterior calculus on smooth manifolds, the exterior derivative and wedge product are natural with respect to smooth maps between manifolds, that is, these operations commute with pullback. In discrete exterior calculus (DEC), simplicial…

In this paper, we introduce coproducts of proximity spaces. After exploring several of their basic properties, we show that given a collection of proximity spaces, the coproduct of their Smirnov compactifications proximally and densely…

We prove that for each Polish space X, the space C(X) of continuous real-valued functions on X satisfies a strong version of the Pytkeev property, if endowed with the compact-open topology. (This shows that whereas it need not be…

In this note we give a simple argument for the fact that the coarse assembly map for a strong coarse homology theory with weak transfers and a bornological coarse space of weakly finite homotopical asymptotic dimension is a phantom…