Related papers: Central extensions and almost representations

The definition and properties of the Euler-Lagrange cohomology groups $H^{2k-1}$, $1 \leqslant k \leqslant n$, on a symplectic manifold $({\cal M}^{2n},\omega)$ are given and studied. For $k = 1$ and $k = n$, they are isomorphic to the…

A result of Dadarlat shows that nonzero even rational cohomology obstructs the matricial stability of many discrete groups. In the author's previous work, 2-cohomology is used to argue that certain groups are not stable in unnormalized…

The cohomology groups of Lie superalgebras and, more generally, of color Lie algebras, are introduced and investigated. The main emphasis is on the case where the module of coefficients is non-trivial. Two general propositions are proved,…

Let $X$ denote the non-compact globally Hermitian symmetric space of type $DIII$, namely, $\text{SO}(n,\mathbb{H})/\text{U}(n)$. Let $\Lambda$ be a uniform torsionless lattice in $\text{SO}(n,\mathbb{H})$. In this note we construct certain…

The canonical trace on the reduced C*-algebra of a discrete group gives rise to a homomorphism from the K-theory of this C^*-algebra to the real numbers. This paper addresses the range of this homomorphism. For torsion free groups, the…

Answering questions of A. Avil\'es, F. Cabello S\'anchez, J. Castillo, M. Gonz\'alez and Y. Moreno we show that the following statements are independent of the usual axioms ZFC with arbitrarily large continuum: for every (some)…

This paper is a new contribution to the partial Galois theory of groups. First, given a unital partial action $\alpha_G$ of a finite group $G$ on an algebra $S$ such that $S$ is an $\alpha_G$-partial Galois extension of $S^{\alpha_G}$ and a…

The homology groups of many natural sequences of groups $\{G_n\}_{n=1}^{\infty}$ (e.g. general linear groups, mapping class groups, etc.) stabilize as $n \rightarrow \infty$. Indeed, there is a well-known machine for proving such results…

Carlson and Toledo conjectured that any infinite fundamental group $\Gamma$ of a compact K\"ahler manifold satisfies $H^2(\Gamma,\R)\not =0$. We assume that $\Gamma$ admits an unbounded reductive rigid linear representation. This…

In this paper we show that certain universal homology classes which are fundamental in topology are algebraic. To be specific, the products of Eilenberg-MacLane spaces ${\cal K}_{2q} \equiv K({\Bbb Z},2) \times K({\Bbb Z}, 4) \times ...…

Let $A$, $A'$ be separable $C^*$-algebras, $B$ a stable $\sigma$-unital $C^*$-algebra. Our main result is the construction of the pairing $[[A',A]]\times\operatorname{Ext}^{-1/2}(A,B)\to\operatorname{Ext}^{-1/2}(A',B)$, where $[[A',A]]$…

We consider a class of quasi-Hopf algebras which we call \emph{generalized twisted quantum doubles}. They are abelian extensions $H = \mb{C}[\bar{G}] \bowtie \mb{C}[G]$ ($G$ is a finite group and $\bar{G}$ a homomorphic image), possibly…

Given a good homology theory E and a topological space X, the E-homology of X is not just an E_{*}-module but also a comodule over the Hopf algebroid (E_{*}, E_{*}E). We establish a framework for studying the homological algebra of…

We show that C*-algebras generated by irreducible representations of finitely generated nilpotent groups satisfy the universal coefficient theorem of Rosenberg and Schochet. This result combines with previous work to show that these…

In this paper we prove that for suitable sequences of congruence subgroups of Bianchi groups, including the standard exhaustive sequences of a congruence subgroup, and even symmetric powers of the standard representation of Sl_2(C) the size…

This paper introduces a canonical Polish groupoid associated to any separable unital C*-algebra, termed the unitary conjugation groupoid. It is defined as the semidirect product of the algebra's dual space by its unitary group, acting by…

We study homotopy epimorphisms and covers formulated in terms of derived Tate's acyclicity for commutative C*-algebras and their non-Archimedean counterparts. We prove that a homotopy epimorphism between commutative C*-algebras precisely…

We develop a new method, based on non-vanishing of second cohomology groups, for proving the failure of lifting properties for full C$^*$-algebras of countable groups with (relative) property (T). We derive that the full C$^*$-algebras of…

Let ${\cal A}_1$ be the class of all unital separable simple $C^*$-algebras $A$ such that $A\otimes U$ has tracial rank at most one for all UHF-algebras of infinite type. It has been shown that amenable ${\cal Z}$-stable $C^*$-algebras in…

Let $\Gamma$ be an abelian group and $g \geq h \geq 2$ be integers. A set $A \subset \Gamma$ is a $C_h[g]$-set if given any set $X \subset \Gamma$ with $|X| = k$, and any set $\{ k_1 , \dots , k_g \} \subset \Gamma$, at least one of the…