Related papers: Central extensions and almost representations

Let U be a connected scheme of finite cohomological dimension in which every finite set of points is contained in an affine open subscheme. Suppose that alpha is a class in H^2(U_et,Gm)_{tors}. For each positive integer m, the K-theory of…

In this paper we show that to a unital associative algebra object (resp. co-unital co-associative co-algebra object) of any abelian monoidal category $\mathcal{C}$ endowed with a symmetric $2$-trace, one can attach a cyclic (resp. cocyclic)…

The goal of this survey is to describe some recent results concerning the L 2 extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity properties. The results presented here are…

We propose a formalism to capture the structure of the equivariant bordism rings of smooth manifolds with commuting involutions. We introduce the concept of an oriented el$_2^{RO}$-algebra, an algebraic structure featuring representation…

Results are obtained on extending flat vector bundles or equivalently general representations from the fundamental group of S, a connected subsurface of the connected boundary of a compact, connected, oriented 3-dimensional manifold, to the…

We introduce a class of novel $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded color superalgebras of infinite dimension. It is done by realizing each member of the class in the universal enveloping algebra of a Lie superalgebra which is a module…

We consider the cohomology group $H^1(\Gamma, \rho)$ of a discrete subgroup $\Gamma\subset G=SU(n, 1)$ and the symmetric tensor representation $\rho$ on $S^m(\mathbb C^{n+1})$. We give an elementary proof of the Eichler-Shimura isomorphism…

We introduce characteristic classes for the spectral sequence associated to a split short exact sequence of Hopf algebras. We show that these characteristic classes can be seen as obstructions for the vanishing of differentials in the…

Given a cohesive sheaf $\Cal S$ over a complex Banach manifold $M$, we endow the cohomology groups $H^q(M,\Cal S)$ of $M$ and $H^q(\frak U,\Cal S)$ of open covers $\frak U$ of $M$ with a locally convex topology. Under certain assumptions we…

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…

One of our result is that 5 measurable sets in $R^8$ always admit an equipartition by 2 hyperplanes. This is an instance of a general equipartition problem (formulated by B. Gr{\" u}nbaum and H. Hadwiger) which can be reduced to the…

An algebra extension A | B is right depth two if its tensor-square A\otimes_B A is in the Dress category Add A as A-B-bimodules. We consider necessary conditions for right, similarly left, D2 extensions in terms of partial A-invariance of…

Let $H$ be the C*-algebra of a non-trivial compact quantum group acting freely on a unital C*-algebra $A$. It was recently conjectured that there does not exist an equivariant $*$-homomorphism from $A$ (type-I case) or $H$ (type-II case) to…

Using higher topos theory, we explore the obstruction to the \v{C}ech-de Rham map being an isomorphism in each degree for diffeological spaces. In degree 1, we obtain an exact sequence which interprets Iglesias-Zemmour's construction from…

Let $G$ be a linear algebraic group over an algebraically closed field of characteristic $p\geq 0$. We show that if $H_1$ and $H_2$ are connected subgroups of $G$ such that $H_1$ and $H_2$ have a common maximal unipotent subgroup and…

We initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using the Ryll-Nardzewski fixed point Theorem, we prove a…

We use braided groups to introduce a theory of $*$-structures on general inhomogeneous quantum groups, which we formulate as {\em quasi-$*$} Hopf algebras. This allows the construction of the tensor product of unitary representations up to…

We consider the finite generation property for cohomology of a finite tensor category C, which requires that the self-extension algebra of the unit Ext*_C(1,1) is a finitely generated algebra and that, for each object V in C, the graded…

We construct some canonically defined central extensions of groups of symplectomorphisms. We show that this central extension is nontrivial in the case of a torus of dimension $\ge 6$ and in the case of a two-dimensional surface of genus…

We study differential forms on an algebraic compactification of a moduli space of metric graphs. Canonical examples of such forms are obtained by pulling back invariant differentials along a tropical Torelli map. The invariant differential…