Related papers: Freeness in higher order frame bundles

Let (G, X) be a transformation group where the group $G$ does not necessarily act freely on the space X. We investigate the extent to which the action of G may fail to be proper. Stability subgroups are used to define new notions of…

A new bound for the rank of the intersection of finitely generated subgroups of a free group is given, formulated in topological terms, and very much in the spirit of Stallings. The bound is a contribution to (although unfortunately not a…

For a general free L\'evy process, we prove the existence of its higher variation processes as limits in distribution, and identify the limits in terms of the L\'evy-It\^o representation of the original process. For a general free compound…

We study the free complexification operation for compact quantum groups, $G\to G^c$. We prove that, with suitable definitions, this induces a one-to-one correspondence between free orthogonal quantum groups of infinite level, and free…

A conjecture of Dicks and the author on rank of the intersection of factor-free subgroups in free products of groups is proved for the case of left ordered groups.

We strengthen Marshall Hall's Theorem to show that free groups are locally extended residually alternating. Let F be any free group of rank at least two, let H be a finitely generated subgroup of infinite index in F and let {g_1,...,g_n} be…

We study the freeness of the group $\mathrm{Inv}(D)$ of invertible ideals of an integral domain $D$, and the freeness of some related groups of (fractional) ideals. We study the relation between $\mathrm{Inv}(D)$ and $\mathrm{Inv}(D_P)$, in…

In this paper, we establish statistical results for a convex co-compact action of a free group on a CAT($-1$) space where we restrict to a non-trivial conjugacy class in the group. In particular, we obtain a central limit theorem where the…

In this article, we consider actions of \mathcal{Z}_+^d, \mathcal{R}_+^d and finitely generated free groups on a von Neumann algebras $M$ and prove a version of maximal ergodic inequality. Additionally, we establish non-commutative…

For any left orderable group G, we recall from work of McCleary that isolated points in the space of left orderings correspond to basic elements in the free lattice ordered group over G. We then establish a new connection between the…

We develop invariants of the lower central series of free groups through linking of letters, showing they span the rational linear dual of the lower central series subquotients. We build on an approach to Lie coalgebras through operads,…

Let $A$ be a subset of a finite field $\mathbb{F}$. When $\mathbb{F}$ has prime order, we show that there is an absolute constant $c > 0$ such that, if $A$ is both sum-free and equal to the set of its multiplicative inverses, then $|A| <…

We give another proof that for every lambda >= beth_omega for every large enough regular kappa < beth_omega we have lambda^{[kappa]}= lambda, dealing with sufficient conditions for replacing beth_omega by aleph_omega. In section 2 we show…

We give some applications of augmentation quotients of free group rings in group theory.

Let $(M,\omega)$ be a connected symplectic manifold on which a connected Lie group $G$ acts properly and in a Hamiltonian fashion with moment map $\mu:M \lra \mf g^*$. Our purpose is investigate multiplicity-free actions, giving criteria to…

We show that any faithful quasi-free actions of a finite group on the Cuntz algebra $\mathcal{O}_\infty$ are mutually conjugate, and that they are asymptotically representable.

For $c\geq 2$, the free centre-by-(nilpotent-of-class-c-1)-by abelian Lie ring on a set $X$ is the quotient $L/[(L')^c,L]$ where $L$ is the free Lie ring on $X$, and $(L')^c$ denotes the $c$th term of the lower central series of the derived…

We consider a notion of bi-freeness for systems of non-commutative random variables with two faces, one of left variables and another of right variables. This includes bi-free convolution operations, bi-free cumulants and the bi-free…

We introduce a modification of Voiculescu's free entropy which coincides with the liminf variant of Voiculescu's free entropy on extremal states, but is a concave upper semi-continuous function on the trace state space. We also extend the…

We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such…