Related papers: Properties of the Solomon homomorphism

We define several versions of the cohomology ring of an associative algebra. These ring structures unify some well known operations from homological algebra and differential geometry. They have some formal resemblance with the quantum…

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…

Let $\psi : G\to GL(V)$ and $\varphi :G \to GL (W)$ be representations of finite group $G$. A linear map $T: V\to W$ is called a morphism from $\psi$ to $\varphi$ if it satisfys $T\psi_g= \varphi_g T$ for each $g\in G$ and let…

In this note, we collect various properties of Seifert homology spheres from the viewpoint of Dehn surgery along a Seifert fiber. We expect that many of these are known to various experts, but include them in one place which we hope to be…

We consider homological finiteness properties $FP_n$ of certain $\mathbb{N}$-graded Lie algebras. After proving some general results, see Theorem A, Corollary B and Corollary C, we concentrate on a family that can be considered as the Lie…

We prove that some skew group algebras have Noetherian cohomology rings, a property inherited from their component parts. The proof is an adaptation of Evens' proof of finite generation of group cohomology. We apply the result to a series…

Let (M,\omega) be a compact symplectic manifold, and \phi be a symplectic diffeomorphism on M, we define a Floer-type homology FH_*(\phi) which is a gen- eralization of Floer homology for symplectic fixed points defined by Dostoglou and…

We construct a subalgebra of dimension $2.3^{n-1}$ of the group algebra of a Weyl group of type $B_n$ containing its Solomon descent's algebra but also the Solomon's descent algebra of the symmetric group. This lead us to a construction of…

We extend the notion of simplicial set with effective homology to diagrams of simplicial sets. Further, for a given finite diagram of simplicial sets $X \colon \mathcal{I} \to \mathsf{sSet}$ such that each simplicial set $X(i)$ has…

We prove that the singular cohomology with finite coefficients of a finite-dimensional Stein space $S$ is isomorphic to the \'etale cohomology of the Stein algebra $\mathcal{O}(S)$. We deduce that any class in $H^k(S,\mathbb{Z})$ comes from…

We prove explicit and elementary formulas for the group homology and cohomology of a finite group with coefficients in any module. We describe in elementary terms the cohomology algebra $H^*(G,k)$ as a graded algebra for a finite group $G$…

Given a Coxeter system $(W,S)$ and a positive real multiparameter $\bq$, we study the "weighted $L^2$-cohomology groups," of a certain simplicial complex $\Sigma$ associated to $(W,S)$. These cohomology groups are Hilbert spaces, as well as…

To a semisimple and cosemisimple Hopf algebra over an algebraically closed field, we associate a planar algebra defined by generators and relations and show that it is a connected, irreducible, spherical, non-degenerate planar algebra with…

We define the homology of a simplicial set with coefficients in a Segal's $\Gamma$-set ($\mathbf S$-module). We show the relevance of this new homology with values in $\mathbf S$-modules by proving that taking as coefficients the $\mathbf…

In arXiv:1605.06672 the authors introduced inhomogeneous bases of the ring of symmetric functions. The elements in these bases have the property that they evaluate to characters of symmetric groups. In this article we develop further…

We obtain some properties of $C^1$ generic surface diffeomorphisms as finiteness of {\em non-trivial} attractors, approximation by diffeomorphisms with only a finite number of {\em hyperbolic} homoclinic classes, equivalence between…

A combinatorial Hopf algebra is a graded connected Hopf algebra over a field $F$ equipped with a character (multiplicative linear functional) $\zeta:H\to F$. We show that the terminal object in the category of combinatorial Hopf algebras is…

This note presents a general theorem about the cohomology of finite dimensional Lie algebras of arbitrary characteristic. As an application we compute the cohomology of the Borel subalgebra of sl(N).

Let $\mathcal A$ and $\mathcal B$ be two (complex) algebras. A linear map $\phi:{\mathcal A}\to{\mathcal B}$ is called $n$-homomorphism if $\phi(a_{1}... a_{n})=\phi(a_{1})...\phi(a_{n})$ for each $a_{1},...,a_{n}\in{\mathcal A}.$ In this…

We obtain the equivariant K-homology of the classifying space \underline{E}W for W a right-angled or, more generally, an even Coxeter group. The key result is a formula for the relative Bredon homology of \underline{E}W in terms of Coxeter…