Related papers: Truncated projective spaces, Brown-Gitler spectra …
To do homological algebra with unbounded chain complexes one needs to first find a way of constructing resolutions. Spaltenstein solved this problem for chain complexes of R-modules by truncating further and further to the left, resolving…
The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…
Let $\A$ be an arrangement of affine lines in $\C^2,$ with complement $\M(\A).$ The (co)homo-logy of $\M(\A)$ with twisted coefficients is strictly related to the cohomology of the Milnor fibre associated to the conified arrangement,…
We study the spectrum of Landau-Ginzburg theories in 1+1 dimensions using the truncated conformal space approach employing a compactified boson. We study these theories both in their broken and unbroken phases. We first demonstrate that we…
We introduce a spherical variant of Milnor's classifying construction for diffeological groups, based on quadratic normalization of barycentric coordinates. This construction gives rise to a contractible diffeological space endowed with…
Given a unital action $\theta $ of an inverse monoid $S$ on an algebra $A$ over a filed $K$ we produce (co)homology spectral sequences which converge to the Hochschild (co)homology of the crossed product $A\rtimes_\theta S$ with values in a…
In this article we use semigroupoids to describe a notion of algebraic bundles, mostly motivated by Fell ($C^*$-algebraic) bundles, and the sectional algebras associated to them. As the main motivational example, Steinberg algebras may be…
Let $t$ be a positive integer. Following work of D. M. Davis, we study the topology of complex-projective product spaces, i.e. quotients of cartesian products of odd dimensional spheres by the diagonal $S^1$-action, and of the $t$-torsion…
It is shown that path algebras modulo relations of the form $\Lambda = KQ/I$, where $Q$ is a quiver, $K$ a coefficient field, and $I \subseteq KQ$ the ideal generated by all paths of a given length, can be readily analyzed homologically,…
Results of Haagerup and Schultz (2009) about existence of invariant subspaces that decompose the Brown measure are extended to a large class of unbounded operators affiliated to a tracial von Neumann algebra. These subspaces are used to…
We consider an interesting class of braidings defined by a combinatorial property in an earlier paper. We show that it consists exactly of those braidings that come from certain Yetter-Drinfeld module structures over pointed Hopf algebras…
We classify various types of graded extensions of a finite braided tensor category $\cal B$ in terms of its $2$-categorical Picard groups. In particular, we prove that braided extensions of $\cal B$ by a finite group $A$ correspond to…
We define a property for restricted Lie algebras in terms of cohomological support and tensor-triangular geometry of their categories of representations. By Tannakian reconstruction, the different symmetric tensor category structures on the…
The two main theorems proved here are as follows: If $A$ is a finite dimensional algebra over an algebraically closed field, the identity component of the algebraic group of outer automorphisms of $A$ is invariant under derived equivalence.…
The numerical invariants (global) cohomological length, (global) cohomological width, and (global) cohomological range of complexes (algebras) are introduced. Cohomological range leads to the concepts of derived bounded algebras and…
We ascertain conditions and structures on categories and semigroups which admit the construction of pseudo-products and trace products respectively, making their connection as precise as possible. This topic is modelled on the ESN Theorem…
We prove the Gromov-Lawson-Rosenberg Conjecture for the group Z/4xZ/4 by computing the connective real k-homology of the classifying space with the Adams spectral sequence and two types of detection theorems for the kernel of the alpha…
The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…
Let H be a quasi-Hopf algebra, a weak Hopf algebra or a braided Hopf algebra. Let B be an H-bicomodule algebra such that there exists a morphism of H-bicomodule algebras v:H\rightarrow B. Then we can define an object B^{co(H)} which is a…
For each integer q>0 there is a cohomology theory such that the zero cohomology group of a manifold N of dimension n is a certain group of cobordism classes of proper fold maps of manifolds of dimension n+q into N. We prove a splitting…