Related papers: On group automorphisms in universal algebraic geom…

We discuss new problems in universal algebraic geometry and explain them by boolean equations.

We study domains in complex $n$-space with automorphism group that does not depend on the full $n$ dimensions of the ambient space. A sufficient geometric condition is obtained to guarantee that a domain has such a "thin" automorphism…

Universal algebraic geometry allows considering of geometric properties of every universal algebra. When two algebras have same algebraic geometry? We must consider the categories of algebraic closed sets of these algebras to answer this…

In this paper, we discuss a group-theoretical generalization of the well-known Gauss formula involving the functionthat counts the number of automorphisms of a finite group. This gives several characterizations of finite cyclic groups.

We study the automorphism group of graphons (graph limits). We prove that after an appropriate "standardization" of the graphon, the automorphism group is compact. Furthermore, we characterize the orbits of the automorphism group on…

We survey results arising from the study of domains in C^n with non-compact automorphism group. Beginning with a well-known characterization of the unit ball, we develop ideas toward a consideration of weakly pseudoconvex (and even…

In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize equational domains, with respect to polynomial equations, inside congruence permutable varieties,…

This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…

This is a systematic exposition of recent results which completely describe the group of automorphisms and the group of autoequivalences of generic analytic K3 surfaces. These groups, hard to determine in the algebraic case, admit a good…

In this note, we consider models in $\mathbb C^2$. The purpose of this note is twofold. We first show a characterization of models in $\mathbb C^2$ by their noncompact automorphism groups. Then we give an explicit description for…

We show that if $K$ is an arbitrary field and $G$ is a finite group then there exists a curve over $K$ with automorphism group $G$. We also give a positive solution to the weak inverse Galois problem for function fields over an arbitrary…

In previous work we determined automorphism groups of cyclic algebraic curves defined over fields of any odd characteristic. In this paper we determine parametric equations of families of curves for each automorphism group for such curves.

We discuss the group of automorphisms of a general MR-algebra. We develop several functors between implication algebras and cubic algebras. These allow us to generalize the notion of inner automorphism. We then show that this group is…

We show that if a field k contains sufficiently many elements(for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic k-group over K is k-isomorphic to Aut(A\otimes_kK), where A is a…

Let $K$ be a field and $f:\mathbb{P}^N \to \mathbb{P}^N$ a morphism. There is a natural conjugation action on the space of such morphisms by elements of the projective linear group $\text{PGL}_{N+1}$. The group of automorphisms, or…

We study the automorphism group of an idempotent evolution algebra, show that any finite group can be the automorphism group of an evolution algebra, and describe certain evolution algebras with given automorphism groups. In particular, we…

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…

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.

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.

The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of…