Related papers: On orbits of automorphism groups on horospherical …
We study automorphism groups of formal matrix algebras. We also consider automorphisms of ordinary matrix algebras (in particular, triangular matrix algebras).
This is a brief overview of a few selected chapters on automorphism groups of affine varieties. It includes some open questions.
The author determines the structure of automorphism groups of smooth plane curves of degree at least four. Furthermore, he gives some upper bounds for the order of automorphism groups of smooth plane curves and classifies the cases with…
Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…
We give several characterisations of groupoids determined by involutive automorphisms on semilattices of groups.
The orbit decomposition is given under the automorphism group on the real split Jordan algebra of all hermitian matrices of order three corresponding to any real split composition algebra, or the automorphism group on the complexification,…
The action of ring automorphisms of the polynomial ring in two variables over the real numbers on real plane curves is considered. The orbits containing degree-three polynomials are computed, with one representative per orbit being…
In this survey, we describe recent progress on asymptotic properties of various automorphic orbits in free groups. In particular, we address the problem of counting potentially positive elements of a given length. We also discuss complexity…
A monomial algebra B is defined as a quotient of a polynomial ring by a monomial ideal, which is an ideal generated by a finite set of monomials. In this paper, we determine the automorphism group of a monomial algebra B, under the…
We characterize the groups isomorphic to full automorphism groups of ordered abelian groups. The result will follow from classical theorems on ordered groups adding an argument from proofs used to realize rings as endomorphism rings of…
We discuss the computation of automorphism groups and normal forms of cones and polyhedra in Normaliz, and indicate its implementation via nauty. The types of automorphisms include integral, rational, Euclidean and combinatorial, as well as…
We classify all smooth projective horospherical varieties with Picard number 1. We prove that the automorphism group of any such variety X acts with at most two orbits and that this group still acts with only two orbits on X blown up at the…
In the paper "Aquino, C., Jim\'enez, R., Mijangos, M., Morales Mel\'endez, Q.: On Invariant (co)homology of a group, preprint" are introduced two groups generated by the orbits of an action of a group on another group by automorphisms. One…
We prove that there is an algorithm to determine whether a tuple of elements in a toral relatively hyperbolic group G is in the automorphic orbit of the other tuple.
We track the trajectories of individual horocycles on the modular surface. Our tracking is constructive, and we thus \emph{effectively} establish topological transitivity and even line-transitivity for the horocyclic flow. We also describe…
We present geometric realizations of horospherical two-orbit varieties, by showing that their blow-up along the unique closed-invariant orbit is the zero locus of a general section of a homogeneous vector bundle over some auxiliary variety.…
The goal of this paper is to present a number of problems about automorphism groups of nonpositively curved polyhedral complexes and their lattices, meant to highlight possible directions for future research.
Consider a smooth connected algebraic group $G$ acting on a normal projective variety $X$ with an open dense orbit. We show that Aut($X$) is a linear algebraic group if so is $G$; for an arbitrary $G$, the group of components of Aut($X$) is…
We investigate analogues of some of the classical results in homogeneous dynamics in non-linear setting. Let $G$ be a closed subgroup of the group of automorphisms of a biregular tree and $\Gamma<G$ a discrete subgroup. For a large class of…
We describe the automorphism groups of elliptic Poisson algebras on polynomial algebras in three variables and give an explicit set of generators and defining relations for this group.