Related papers: Non-microstates free entropy dimension for groups

Let S=K[X_1,...,X_n] be the polynomial ring over a field K. For bounded below Z^n-graded S-modules M and N we show that if Tor^S_p(M,N) is nonzero, then for every i between 0 and p, the dimension of the K-vector space Tor^S_i(M,N) is at…

We use free groups to settle a couple questions about the values of the Pimsner-Popa-Voiculescu modulus of quasidiagonality for a set of operators $\Omega$, denoted by qd$(\Omega)$. Along the way we deduce information about the operator…

We show that for any positive integer $n$ there exists a constant $C(n)>0$ such that any $n$-generated group $G$, which acts by isometries on a $\delta$-hyperbolic space (with $\delta>0$), is either free or has a nontrivial element with…

We present a fast algorithm to compute the Delta set of a nonsymmetric numerical semigroups with embedding dimension three.

The first $\ell^2$ Betti number of a group is non-decreasing under various embeddings arising from first order logic. Strict inequality is proved for elementary embeddings of non-abelian proper subgroups within torsion free hyperbolic…

We introduce a parameter space containing all algebraic integers $\beta\in(1,2]$ that are not Pisot or Salem numbers, and a sequence of increasing piecewise continuous function on this parameter space which gives a lower bound for the…

In this note we study sets of normal generators of finitely presented residually $p$-finite groups. We show that if an infinite, finitely presented, residually $p$-finite group $G$ is normally generated by $g_1,\dots,g_k$ with order…

In this paper we prove that any full Perazzo algebra $A_F$, whose Macaulay dual generator is a Perazzo form $F\in K[X_0,\dots,X_n,U_1,\dots,U_m]_d$ with $n+1 = \binom{d+m-2}{m-1}$, is the doubling of a 0-dimensional scheme in $\PP^{n+m}$…

We investigate the standard generalized Gorenstein algebras of homological dimension three, giving a structure theorem for their resolutions. Moreover in many cases we are able to give a complete description of their graded Betti numbers.

The geometric dimension for proper actions $\underline{\mathrm{gd}}(G)$ of a group $G$ is the minimal dimension of a classifying space for proper actions $\underline{E}G$. We construct for every integer $r\geq 1$, an example of a virtually…

This paper is a continuation of our work on D. Voiculescu's topological free entropy dimension in unital C*-algebras. In this paper we first prove the topological free entropy dimension of a MF-nuclear and inner QD algebra is irrelevant to…

We get stationary solutions of a free stochastic partial differential equation. As an application, we prove equality of non-microstate and microstate free entropy dimensions under a Lipschitz like condition on conjugate variables, assuming…

We derive polynomial identities of arbitrary degree $n$ for syzygies degrees of numerical semigroups S_m=<d_1,...,d_m> and show that for n>=m they contain higher genera G_r=\sum_{s\in Z_>\setminus S_m}s^r of S_m. We find a number…

Certain classes of automorphisms of recued amalgamated free products of C*-algebras are shown to have Brown-Voiculescu topological entropy zero. Also, for automorphisms of exact C*-algebras, the Connes-Narnhofer-Thirring entropy is shown to…

Let $d \geq 3$ be a natural number. We show that for all finite, non-empty sets $A \subseteq \mathbb{R}^d$ that are not contained in a translate of a hyperplane, we have \[ |A-A| \geq (2d-2)|A| - O_d(|A|^{1- \delta}),\] where $\delta >0$ is…

We develop a geometric procedure for finding the Ap\'ery set of any numerical semigroup with embedding dimension four. Previous methods of comparable strength worked only for embedding dimension three or under very specific conditions. We…

For a nilpotent group $G$, let $\Xi(G)$ be the difference between the complement of the generating graph of $G$ and the commuting graph of $G$, with vertices corresponding to central elements of $G$ removed. That is, $\Xi(G)$ has vertex set…

For a torsion free finitely generated nilpotent group G we naturally associate four finite dimensional nilpotent Lie algebras over a field of characteristic zero. We show that if G is a relatively free group of some variery of nilpotent…

Suppose that G is a nontrivial torsion-free group and w is a word over the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\}. It is proved that for n\ge2 the group \~G=<G,x_1,x_2,...,x_n | w=1> always contains a nonabelian free subgroup. For n=1…

We show that the nuclear dimension of a (twisted) group C*-algebra of a virtually polycyclic group is finite. This prompts us to make a conjecture relating finite nuclear dimension of group C*-algebras and finite Hirsch length, which we…