Related papers: Homotopy formulas for cyclic groups acting on ring…

We apply categorical machinery to the problem of defining cyclic cohomology with coefficients in two particular cases, namely quasi-Hopf algebras and Hopf algebroids. In the case of the former, no definition was thus far available in the…

The aim of this note is to show that the cycle decomposition of elements of the symmetric group admits a quite natural formulation in the framework of dual Coxeter theory, yielding a generalization of it to the family of so-called parabolic…

In this article, we prove the algebraic counterpart of the topological results $H^1(S^1, \mathbb{Z}) \cong \mathbb{Z}$ and $H^1(S^2, \mathbb{Z}) \cong \{0\}$. We also see that a non-trivial element of the algebraic cohomotopy groups of…

The explicit expression of all the WZW effective actions for a simple group G broken down to a subgroup H is established in a simple and direct way, and the formal similarity of these actions to the Chern-Simons forms is explained.…

We study a naturally occurring $E_{\infty}$-subalgebra of the full $E_2$-Hochschild cochain complex arising from coherent cochains. For group rings and certain category algebras, these cochains detect $H^*(B {\cal{C}})$, the simplicial…

These notes illustrates the power of formulating ideas of commutative algebra in a homotopy invariant form. They can then be applied to derived categories of rings or ring spectra. These ideas are powerful in classical algebra, in…

When the standard representation of a crystallographic Coxeter group is reduced modulo an odd prime p, one obtains a finite group G^p acting on some orthogonal space over Z_p . If the Coxeter group has a string diagram, then G^p will often…

We study the relations between partial and global group cohomology with values in a commutative unital ring $\mathcal{A}$. In particular, for a unital partial action of a group $G$ on $\mathcal{A}$, such that $\mathcal{A}$ is a direct…

We study the vanishing of (co)homology along ring homomorphisms for modules that admit certain filtrations, and generalize a theorem of O. Celikbas-Takahashi. Our work produces new classes of rigid and test modules, in particular over local…

Let $G$ be a group acting freely, properly discontinuously and cellularly on a finite dimensional $C$W-complex $\Sigma(2n)$ which has the homotopy type of the $2n$- sphere $\mathbb{S}^{2n}$. Then, this action induces an action of the group…

We describe the groups that have the same holomorph as a finite perfect group. Our results are complete for centerless groups. When the center is non-trivial, some questions remain open. The peculiarities of the general case are illustrated…

A cyclic cohomology theory adapted to Hopf algebras has been introduced recently by Connes and Moscovici. In this paper, we consider this object in the homological framework, in the spirit of Loday-Quillen and Karoubi's work on the cyclic…

A $(G,n)$-complex is an $n$-dimensional CW-complex with fundamental group $G$ and whose universal cover is $(n-1)$-connected. If $G$ has periodic cohomology then, for appropriate $n$, we show that there is a one-to-one correspondence…

We define homotopy group actions in terms of families of $A_\infty$ algebras indexed by a manifold M. We give explicit formulae for the $A_\infty$ morphism induced by a path on the manifold and for the $A_\infty$ homotopy corresponding to a…

Let $G$ be a group scheme of finite type over a field, and consider the cohomology ring $H^*(G)$ with coefficients in the structure sheaf. We show that $H^*(G)$ is a free module of finite rank over its component of degree 0, and is the…

I investigate modal group theory for arbitrary homomorphisms. Possibility is interpreted by the existence of a group homomorphism out of the given group, so the semantics is governed by the possibility of collapse: elements may be…

We consider the hidden subgroup problem on the semi-direct product of cyclic groups $\Z_{N}\rtimes\Z_{p}$ with some restriction on $N$ and $p$. By using the homomorphic properties, we present a class of semi-direct product groups in which…

The action of the idempotent deformations on finite groups is discussed. This action is described in terms of the homological properties of groups. The orbits of finite simple groups are determined.

We show by a direct computation that, for any Hopf algebra with a modulus-like character, the formulas first introduced in [CM] in the context of characteristic classes for actions of Hopf algebras, do define a cyclic module. This provides…

A group $\Gamma$ is defined to be cofinitely Hopfian if every homomorphism $\Gamma\to\Gamma$ whose image is of finite index is an automorphism. Geometrically significant groups enjoying this property include certain relatively hyperbolic…