Related papers: Abelian subgroups of two-dimensional Artin groups
Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC type Artin groups. We show that the class of…
Abelian groups having partial orderings compatible with their binary operations have long been studied in the literature. In particular, lattice-ordered abelian groups constitute a universal-algebraic variety, and thus form a category which…
Given an abelian variety over a field with a discrete valuation, Grothendieck defined a certain open normal subgroup of the absolute inertia group. This subgroup encodes information on the extensions over which the abelian variety acquires…
It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology.
In this work, we classify the group gradings on finite-dimensional incidence algebras over a field, where the field has characteristic zero, or the characteristic is greater than the dimension of the algebra, or the grading group is…
We classify affine varieties with an action of a connected, reductive algebraic group such that the group is isomorphic to an open orbit in the variety. This is accomplished by associating a set of one-parameter subgroups of the group to…
We explore algebraic characterizations of 2-knots whose associated knot manifolds fibre over lower-dimensional orbifolds, and consider also some issues related to the groups of higher-dimensional fibred knots.
In this paper, we construct embeddings of right-angled Artin groups into higher dimensional Thompson groups. In particular, we embed every right-angled Artin groups into n-dimensional Thompson group, where n is the number of complementary…
We give a necessary and sufficient condition on a visual splitting of an Artin group satisfying the conditions of two well known conjectures to be acylindrical, and demonstrate how this can be used to provide a large class of novel examples…
We perform a complete classification of all 56 subgroups of the two-qubit Clifford group containing the two-qubit Pauli group. We provide generators for these groups using gates familiar to the quantum information community and we reference…
In the current paper we study the groups, whose subnormal abelian subgroups are normal. We obtained a quite detailed description of such hyperabelian groups with a periodic Baer radical. The description of hyperabelian Lie algebras, whose…
In this paper we solve the isomorphism problem for all large-type Artin groups. Our strategy involves reconstructing the Coxeter groups associated with large-type Artin groups in a purely algebraic way. This answers several questions raised…
We describe the structure of quasiflats in two-dimensio\-nal Artin groups. We rely on the notion of metric systolicity developed in our previous work. Using this weak form of non-positive curvature and analyzing in details the combinatorics…
This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the varieties of Jordan, Lie and associative algebras.
We prove an analogue of the Centralizer Theorem in the context of Artin-Tits groups.
We use rigid analytic uniformization by Schottky groups to give a bound for the order of the abelian subgroups of the automorphism group of a Mumford curve in terms of its genus.
A complete classification of two-dimensional algebras over algebraically closed fields is provided
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
We obtain a complete description of the integer group determinants for the non-abelian groups of order 18.
We give a presentation of abelian class field theory.