Related papers: Abelian subgroups of two-dimensional Artin groups
We classify closed abelian subgroups of the automorphism group of any compact classical simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup, and describe Weyl groups of maximal abelian subgroups.
We present a complete classification for the epimorphisms from the affine Artin-Tits groups $A(\widetilde{A}_{n})$ to the corresponding Coxeter groups $W(\widetilde{A}_{n})$, for $n\geq 1$.
We prove that any standard parabolic subgroup of any Artin group is convex with respect to the standard generating set.
We give a characterization of Bestvina--Brady groups split over abelian subgroups and describe a JSJ-decomposition of Bestvina--Brady groups.
We prove that any left-ordered inp-minimal group is abelian, and we provide an example of a non-abelian left-ordered group of dp-rank 2.
We classify, up to isomorphism and up to equivalence, involutions on graded-division finite-dimensional simple real (associative) algebras, when the grading group is abelian.
We give a sharp bound for orders of elementary abelian 2-groups of birational automorphisms of rationally connected threefolds.
We study abelian subgroups of Galois groups of function fields.
We provide an explicit presentation of the automorphism group of an edge-separated CLTTF Artin group.
The abstract will be added in due course.
In this paper we study (logical) types and isotypical equivalence of torsion free Abelian groups. We describe all possible types of elements and standard 2-tuples of elements in these groups and classify separable torsion free Abelian…
We find a condition on the underlying graph of an Artin group that fully determines if it is subgroup separable. As a consequence, an Artin group is subgroup separable if and only if it can be obtained from Artin groups of ranks at most 2…
We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.
We introduce and investigate the ribbon groupoid associated with a Garside group. Under a technical hypothesis, we prove that this category is a Garside groupoid. We decompose this groupoid into a semi-direct product of two of its parabolic…
We classify abelian subgroups of Out(F_n) up to finite index in an algorithmic and computationally friendly way. A process called disintegration is used to canonically decompose a single rotationless element \phi into a composition of…
We consider two variants of those Abelian groups with all proper strongly invariant subgroups isomorphic and give an in-depth study of their basic and specific properties in either parallel or contrast to the Abelian groups with all proper…
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 describe some of the basic properties of the 2-category of 2-term complexes in an abelian category, using butterflies as morphisms.
We classify the Artin groups that admit retractions onto all of their parabolic subgroups. Our approach relies on a detailed analysis of triangular subgroups, with a key ingredient being the classification of homomorphisms between dihedral…
A hypergroup is called an elementary abelian 2-hypergroup if it is a constrained direct product of the closed subsets of two elements. In this paper, the elementary abelian 2-hypergroups are studied. All closed subsets and all strongly…