Related papers: Automorphism groups of combinatorial Hantzsche-Wen…
Combinatorial Hantzsche-Wendt groups G(n) were defined by W. Craig and P. A. Linnell. For n = 2 it is a fundamental group of 3-dimensional oriented flat manifold with no cyclic holonomy group. We calculate the Hilbert-Poincare series of…
We study the family of closed Riemannian n-manifolds with holonomy group isomorphic to $Z_2^{n-1}$, which we call generalized Hantzsche-Wendt manifolds. We prove results on their structures, compute some invariants, and find relations…
There are only 10 Euclidean forms, that is flat closed three dimensional manifolds: six are orientable $\mathcal{G}_1,\dots,\mathcal{G}_6$ and four are non-orientable $\mathcal{B}_1,\dots,\mathcal{B}_4$. In the present paper we investigate…
Complex Hantzsche-Wendt manifolds are flat K\"ahler manifolds with holonomy group $\mathbb{Z}_2^{n-1}\subset SU(n)$. They are important example of Calabi-Yau manifolds of abelian type. In this paper we describe them as quotients of a…
Bergman has given the following abstract characterisation of the inner automorphisms of a group $G$: they are exactly those automorphisms of $G$ which can be extended functorially along any homomorphism $G \rightarrow H$ to an automorphism…
A combinatorial map is a connected topological graph cellularly embedded in a surface. This monograph concentrates on the automorphism group of a map, which is related to the automorphism group of a Klein surface and a Smarandache manifold,…
We describe the outer automorphism group of a one-ended fundamental group of a graph of groups, when edge groups are cyclic, and vertex groups are torsion-free with cyclic centralizers. We show that in this case the outer automorphism group…
This mainly expository article is devoted to recent advances in the study of dynamical aspects of the Cuntz algebras O_n, with n finite, via their automorphisms and, more generally, endomorphisms. A combinatorial description of permutative…
We investigate the combinatorial and geometric properties of automorphism groups of universal right-angled Coxeter groups, which are the automorphism groups of free products of copies of Z_2. It is currently an open question as to whether…
The Cuntz-Toeplitz algebra $E_{n+1}$ for $n\geq1$ is the universal C*-algebra generated by $n+1$ isometries with mutually orthogonal ranges. In this paper, we investigate the automorphism groups of the Cuntz-Toeplitz algebras and determine…
By Hantzsche-Wendt manifold (for short HW-manifold) we understand any oriented closed Riemannian manifold of dimension n with a holonomy group (Z_2)^{n-1}. Two HW-manifolds M_1 and M_2 are cohomological rigid if and only if a homeomorphism…
For any given finite group, Schulte and Williams (2015) establish the existence of a convex polytope whose combinatorial automorphisms form a group isomorphic to the given group. We provide here a shorter proof for a stronger result: the…
We survey recent results on endomorphisms and especially on automorphisms of the Cuntz algebras O_n, with a special emphasis on the structure of the Weyl group. We discuss endomorphisms globally preserving the diagonal MASA and their…
Zonotopal algebras (external, central, and internal) of an undirected graph G introduced by Postnikov-Shapiro and Holtz-Ron, are finite-dimensional commutative graded algebras whose Hilbert series contain a wealth of combinatorial…
The Weyl group of the Cuntz algebra O_n, with n finite, is investigated. This is (isomorphic to) the group of polynomial automorphisms of O_n, namely those induced by unitaries that can be written as finite sums of words in the canonical…
We investigate the group structure of center-preserving automorphisms of the finite Heisenberg group over $\mathbb Z_N$ with $U(1)$ extension, which arises in finite-dimensional quantum mechanics on a discrete phase space. Constructing an…
The inner automorphisms of a group G can be characterized within the category of groups without reference to group elements: they are precisely those automorphisms of G that can be extended, in a functorial manner, to all groups H given…
We give elementary proofs of the following two theorems on automorphisms of a finite group G: (1) An automorphism of G is inner if and only if it extends to an automorphism of every finite group containing G. (2) There exists a finite…
The Hasse Weil bound restricts the number of points of a curve which are defined over a finite field; if the number of points meets this bound, the curve is called maximal. Giulietti and Korchmaros introduced a curve C_3 which is maximal…
A graphs of rank n (homotopy equivalent to a wedge of n circles) without ``separating edges'' has a canonical n-dimensional compact C^1 manifold thickening. This implies that the canonical homomorphism f:Out(F_n)-> GL(n,Z) is trivial in…