For G ≤ Sym(Ω), let π(G) be the set of partitions of Ω given by the cycles of elements of G. Under the refinement order, π(G) admits join and meet operations. We say thatG is joinor meet-coherent if π(G) is joinor meet-closed, respectively. The centralizer in Sym(Ω) of any permutation g is shown to be meetcoherent, and join-coherent subject to a finiteness condition. Hence if G is a centralizer...

We develop and collect techniques for determining Hochschild cohomology of skew group algebras S(V )#G and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer subgroups, focusing on the infinite family of complex reflection groups G(r, p, n) to illustrate our ideas. Resulting formulas for Hochschild two-cocycles give i...

A p–compact group (see Dwyer–Wilkerson [8]) is a loop space X such that X is Fp –finite and that its classifying space BX is Fp –complete (see Andersen–Grodal– Møller–Viruel [2] and Dwyer–Wilkerson [11]). We recall that the p–completion of a compact Lie group G is a p–compact group if π0(G) is a p–group. Next, if C(ρ) denotes the centralizer of a group homomorphism ρ from a p–toral group to a c...

By constructing, in the relative case, objects analoguous to Rips and Sela’s canonical representatives, we prove that the set of conjugacy classes of images by morphisms without accidental parabolic, of a finitely presented group in a relatively hyperbolic group, is finite. An important result of W.Thurston is : Theorem 0.1 ([T] 8.8.6) Let S be any hyperbolic surface of finite area, and N any g...

A version of non-stationary normal forms theory was recently obtained by M. Guysinsky and A. Katok, which has become an important ingredient in several recent investigations of rigidity of group actions. Our main aim is to explain their results, the sub-resonance normal forms and centralizer theorems, from a differential-geometric perspective.

Let W be a right-angled Coxeter group. We characterize the centralizer of the Coxeter element of a finite special subgroup of W. As an application, we give a solution to the generalized word problem for Inn(W ) in Aut(W ). Mathematics Subject Classification: 20F10, 20F28, 20F55

On the torus of dimension 2, 3, or 4, we show that the subset of diffeomorphisms with trivial centralizer in the C topology has nonempty interior. We do this by developing two approaches, the fixed point and the odd prime periodic point, to obtain trivial centralizer for an open neighbourhood of Anosov diffeomorphisms arbitrarily near certain irreducible hyperbolic toral automorphism.

For a finite connected simple graph, the Terwilliger algebra is matrix generated by adjacency and idempotents corresponding to distance partition with respect fixed vertex. We will consider algebras defined two other partitions centralizer of stabilizer vertex in automorphism group graph. give some methods compute such examples for various graphs.

The normalizer NW (WJ) of a standard parabolic subgroup WJ of a finite Coxeter group W splits over the parabolic subgroup with complement NJ consisting of certain minimal length coset representatives of WJ in W . In this note we show that (with the exception of a small number of cases arising from a situation in Coxeter groups of type Dn) the centralizer CW (w) of an element w ∈ W is in a simil...