Related papers: A short note about diffuse Bieberbach groups

We give a classification of minimal algebras generated in degree 1, defined over any field $\bk$ of characteristic different from 2, up to dimension 6. This recovers the classification of nilpotent Lie algebras over $\bk$ up to dimension 6.…

We develop new techniques to classify basic algebras of blocks of finite groups over algebraically closed fields of prime characteristic. We apply these techniques to simplify and extend previous classifications by Linckelmann, Murphy and…

The complete affine structures on abelian Lie algebras in small dimensions are well known. In this paper we are interested by the non complete case. In particular we classify all these structures in dimensions 2 and 3.

We complete the classification of the 6-dimensional quasi-Hopf algebras, by proving that any such algebra is semisimple. As byproducts, we provide examples of 6-dimensional quasi-bialgebras that are not semisimple as algebras, as well as…

To a finite group $G$, one can associate several notions of dimensions (or degrees). In this survey, we attempt to bring together some of the notions of dimensions or degrees defined using representations of the group in General Linear…

We study the minimal dimension of the classifying space of the family of virtually cyclic subgroups of a discrete group. We give a complete answer for instance if the group is virtually poly-Z, word-hyperbolic or countable locally virtually…

We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach-Lie groups and some monothetic subgroups of the unitary group of a separable…

Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the so-called DDVV inequality which relates the scalar curvature, the mean curvature and the normal scalar curvature. This property is conformal…

The object of investigation are Lie groups considered as almost contact B-metric manifolds of the lowest dimension three. It is established a correspondence of all basic-class-manifolds of the Ganchev-Mihova-Gribachev classification of the…

We classify quasi-simple finite groups of essential dimension 3.

Combinatorial aspects of R-subgroups of finite dimensional Beidleman near-vector spaces over nearfields are studied. A characterization of R-subgroups is used to obtain the smallest possible size of a generating set of a subgroup, which is…

Following an idea of Gon\c{c}alvez, Guaschi and Ocampo on the usual braid group we construct crystallographic and Bieberbach groups as (sub)quotients of the generalized braid group associated to an arbitrary complex reflection group.

We state a number of open questions on 3-dimensional Poincar\'e duality groups and their subgroups, motivated by considerations from 3-manifold topology.

In this paper we give a complete classification of the Leibniz algebras of biderivations of right Leibniz algebras of dimension up to three over a field $\mathbb{F}$, with $\operatorname{char}(\mathbb{F})\neq 2$. We describe the main…

In this paper we show that some 3-dimensional isometry algebras, specifically those of type I, II, III and V (according Bianchi's classification), can be obtained as expansions of the isometries in 2 dimensions. It is shown that in general…

The subspace structure of Beidleman near-vector spaces is investigated. We characterise finite dimensional Beidleman near-vector spaces and we classify the R-subgroups of finite dimensional Beidleman near-vector spaces. We provide an…

This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…

In this paper we consider convex co-compact subgroups of the projective linear group. We prove that such a group is relatively hyperbolic with respect to a collection of virtually Abelian subgroups of rank two if and only if each open face…

We classify finite-dimensional complex Hopf algebras $A$ which are pointed, that is, all of whose irreducible comodules are one-dimensional, and whose group of group-like elements $G(A)$ is abelian such that all prime divisors of the order…

We investigate the behavior of small subsets of causal sets that approximate Minkowski space in three, four, and five dimensions, and show that their effective dimension decreases smoothly at small distances. The details of the short…