Commuting diagrams for the TNT elements on cubes

On the Centralizer of the Sum of Commuting Nilpotent Elements

Let X and Y be commuting nilpotent K-endomorphisms of a vector space V , where K is a field of characteristic p ≥ 0. If F = K(t) is the field of rational functions on the projective line P1/K , consider the K(t)-endomorphism A = X+ tY of V . If p = 0, or if A = 0, we show here that X and Y are tangent to the unipotent radical of the centralizer of A in GL(V ). For all geometric points (a : b) o...

Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements

Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...

On Spaces of Commuting Elements in Lie Groups

The purpose of this paper is to introduce a new method of “stabilizing” spaces of homomorphisms Hom(π,G) where π is a certain choice of finitely generated group and G is a compact Lie group. The main results apply to the space of all ordered n-tuples of pairwise commuting elements in a compact Lie group G, denoted Hom(Zn, G), by assembling these spaces into a single space for all n ≥ 0. The res...

Almost commuting elements in compact Lie groups

On Commuting Elements and Embeddings of Graph Groups and Monoids

We study commutation properties of subsets of right-angled Artin groups and trace monoids. We show that if Γ is any graph not containing a four-cycle without chords, then the group G(Γ) does not contain four elements whose commutation graph is a four-cycle; a consequence is that G(Γ) does not have a subgroup isomorphic to a direct product of non-abelian free groups. We also obtain corresponding...