Related papers: Tracing projective modules over noncommutative orb…

We prove that generic homologically nontrivial $(2n-1)$-parameter family of analytic discs attached by their boundaries to a CR manifold $\Omega$ in $\mathbb C^n, n \le 2$ tests CR functions: if a smooth function on $\Omega$ extends…

We extend Masuoka's Theorem [11] concerning the isomorphism between the group of invertible bimodules in a non-commutative ring extension and the group of automorphisms of the associated Sweedler's canonical coring, to the class of finite…

Starting from a (small) rigid C$^*$-tensor category $\mathscr{C}$ with simple unit, we construct von Neumann algebras associated to each of its objects. These algebras are factors and can be either semifinite (of type II$_1$ or II$_\infty$,…

For a twisted partial action \Theta of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A X_\Theta G is proved to be associative. Given a G-graded k-algebra B =…

We study finitely generated projective modules over noncommutative tori. We prove that for every module $E$ with constant curvature connection the corresponding element $[E]$ of the K-group is a generalized quadratic exponent and,…

Let $A$ be a complex torus and $G$ a finite group acting on $A$ without translations such that $A/G$ is smooth. Consider the subgroup $F\leq G$ generated by elements that have at least one fixed point. We prove that there exists a point…

We introduce and analyse a new type of quantum 2-spheres. Then we apply index theory for noncommutative line bundles over these spheres to conclude that quantum lens spaces are non-crossed-product examples of principal extensions of…

The orbifold construction $A\mapsto A^G$ for a finite group $G$ is fundamental in rational conformal field theory. The construction of $Rep(A^G)$ from $Rep(A)$ on the categorical level, often called gauging, is also prominent in the study…

Let A#_{\alpha, \omega}H be a partial crossed product. In this paper, we first generalize the theorem about the existence of an enveloping action to twisted partial actions. Second, we construct a Morita context between the partial crossed…

Let (G) be a connected compact non-abelian Lie-group and (T) a maximal torus of (G). A torus manifold with (G)-action is defined to be a smooth connected closed oriented manifold of dimension (2\dim T) with an almost effective action of (G)…

We show that the cyclic and epicyclic categories which play a key role in the encoding of cyclic homology and the lambda operations, are obtained from projective geometry in characteristic one over the infinite semifield F of "max-plus…

We establish a connection between the representation theory of certain noncommutative singular varieties and two-dimensional lattice models. Specifically, we consider noncommutative biparametric deformations of the fiber product of two…

We define "tracial" analogs of the Rokhlin property for actions of finite groups, approximate representability of actions of finite abelian groups, and of approximate innerness. We prove four analogs of related "nontracial" results. First,…

To study outer actions $\a$ of a group $G$ on a factor $\sM$ of type {\threel}, $0<\la<1$, we study first the cohomology group of a group with the unitary group of an abelian {\vna} as a coefficient group and establish a technique to reduce…

We prove a criterion of when a coaction of a compact Lie group on an algebra of continuous functions on a compact manifold extends to a coaction of deformation quantizations of the Lie group and the algebra. We compute an explicit example…

A Lie group G is called a trace class group if for every irreducible unitary representation R of G and every C-infinity function f with compact support the operator R(f) is of trace class. In this note we prove that the semidirect product…

We show that log flat torsors over a family $X/S$ of nodal curves under a finite flat commutative group scheme $G/S$ are classified by maps from the Cartier dual of $G$ to the log Jacobian of $X$. We deduce that fppf torsors on the smooth…

Given an abelian $p$-group $G$ of rank $n$, we construct an action of the torus $\mathbb{T}^n$ on the stable module $\infty$-category of $G$-representations over a field of characteristic $p$. The homotopy fixed points are given by the…

In this paper we study the actions of tori (standard compact tori, as well as their quaternionic analogues) on products of spheres. It is proved that the orbit space of a specific action of a torus on a product of spheres is homeomorphic to…

We show that a large class of maximally degenerating families of n-dimensional polarized varieties come with a canonical basis of sections of powers of the ample line bundle. The families considered are obtained by smoothing a reducible…