相关论文: Roe bimodules as morphisms of discrete metric spac…

We discover a class of projective self-dual algebraic varieties. Namely, we consider actions of isotropy groups of complex symmetric spaces on the projectivized nilpotent varieties of isotropy modules. For them, we classify all orbit…

We investigate when the categories of all rational $A$-modules and of finite dimensional rational modules are closed under extensions inside the category of $C^*$-modules, where $C^*$ is the cofinite topological completion of $A$. We give a…

For a fixed finite group $Q$ and semi-simple finite dimensional algebra $S$, we examine an equivalence between strongly $Q$-graded algebras (extensions) with identity component $S$ and $S^1$-gerbes on action groupoids of $Q$ on the set of…

Basic definitions and properties of nearly associative algebras are described. Nearly associative algebras are proved to be Lie-admissible algebras. Two-dimensional nearly associative algebras are classified, and its main classes are…

Let $\cal M$ be a Banach C*-module over a C*-algebra $A$ carrying two $A$-valued inner products $< .,. >_1$, $<.,. >_2$ which induce equivalent to the given one norms on $\cal M$. Then the appropriate unital C*-algebras of adjointable…

We analyze the dichotomy amenable/paradoxical in the context of (discrete, countable, unital) semigroups and corresponding semigroup rings. We consider also F{\o}lner's type characterizations of amenability and give an example of a…

For a finite dimensional algebra $A$, we prove that the bounded homotopy category of projective $A$-modules and the bounded derived category of $A$-modules are dual to each other via certain categories of locally-finite cohomological…

We show that any Abelian module category over the (degenerate or quantum) Heisenberg category satisfying suitable finiteness conditions may be viewed as a 2-representation over a corresponding Kac-Moody 2-category (and vice versa). This…

We consider the classification, up to unitary equivalence, of commuting n-tuples of isometries. We pay special attention to the case when the product of the isometries is a shift of finite multiplicity, and we provide a complete…

Let n be a positive integer, and let R be a finitely presented (but not necessarily finite dimensional) associative algebra over a computable field. We examine algorithmic tests for deciding (1) if every n-dimensional representation of R is…

We study varieties of complexes of projective modules with fixed ranks, and relate these varieties to the varieties of their homologies. We show that for an algebra of global dimension at most two, these two varieties are related by a pair…

We introduce almost diagonal matrices in the setting of (anisotropic) discrete homogeneous Triebel-Lizorkin type spaces and homogeneous modulation spaces, and it is shown that the class of almost diagonal matrices is closed under matrix…

In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called…

The Modular Isomorphism Problem asks if an isomorphism of group algebras of two finite p-groups G and H over a field of characteristic p, implies an isomorhism of the groups G and H. We survey the history of the problem, explain strategies…

In this paper we study loops, neardomains and nearfields from a categorical point of view. By choosing the right kind of morphisms, we can show that the category of neardomains is equivalent to the category of sharply 2-transitive groups.…

Let $\V$ be a mixed characteristic complete discrete valuation ring, let $\X$ and $\Y$ be two smooth formal $\V$-schemes, let $f_0$ : $X \to Y$ be a projective morphism between their special fibers, let $T$ be a divisor of $Y$ such that…

In this paper we provide explicit dual Ramsey statements for several classes of finite relational structures (such as finite linearly ordered graphs, finite linearly ordered metric spaces and finite posets with a linear extension) and…

To define enumerative invariants in geometry, one often needs orientations on moduli spaces of geometric objects. This monograph develops a new bordism-theoretic point of view on orientations of moduli spaces. Let $X$ be a manifold with…

In a previous paper the authors developed a H^1-BMO theory for unbounded metric measure spaces $(M,\rho,m)$ of infinite measure that are locally doubling and satisfy two geometric properties, called "approximate midpoint" property and…

We study IE-closed subcategories of a module category, subcategories which are closed under taking Images and Extensions. We investigate the relation between IE-closed subcategories and torsion pairs, and characterize $\tau$-tilting finite…