Related papers: Groupoids Determined by Involutive Automorphisms o…

We prove some general results concerning the size of the group of automorphisms of the Douady space of points on a surface. We then study some properties of the automorphisms coming from an automorphism of the surface, in particular their…

Given a positive definite even lattice and a commutative ring, there is a standard construction of a lattice vertex algebra over the commutative ring, and it admits a natural grading by non-negative integers. We describe the groups of…

We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm…

Topological characterization of torus groups is given.

We introduce a new kind of groupoid--a pseudo \'etale groupoid, which provides many interesting examples of noncommutative Poisson algebras as defined by Block, Getzler, and Xu. Following the idea that symplectic and Poisson geometries are…

It is known that, for the algebra of functions on a Kleinian singularity, the parameter space of deformations and the parameter space of quantizations coincide. We prove that, for a Kleinian singularity of type $\mathbf{A}$ or $\mathbf{D}$,…

We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids. We compare the holomorph with the monoid of mappings that preserve the ternary heap…

A notion of degeneration of elements in groups is introduced. It is used to parametrize the orbits in a finite abelian group under its full automorphism group by a finite distributive lattice. A pictorial description of this lattice leads…

We classify all possible automorphism groups of smooth cubic surfaces over an algebraically closed field of arbitrary characteristic. As an intermediate step we also classify automorphism groups of quartic del Pezzo surfaces. We show that…

This paper is devoted to a study of the automorphism groups of three series of finite dimensional special odd Hamiltonian superalgebras $\mathfrak{g}$ over a field of prime characteristic. Our aim is to characterize the connections between…

We prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.

We complete the classification of automorphism groups of del Pezzo surfaces over algebraically closed fields of odd positive characteristic.

We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades. The main themes are: the small index property in the countable and uncountable cases; the…

Introducing the deformation theory of holomorphic Cartan geometries, we compute infinitesimal automorphisms and infinitesimal deformations. We also prove the existence of a semi-universal deformation of a holomorphic Cartan geometry.

These lecture notes provide an introduction to automorphism groups of graphs. Some special families of graphs are then discussed, especially the families of Cayley graphs generated by transposition sets.

We settle the automorphism groups of curves appearing in a classification list of smooth plane curves with at least two Galois points. One of them is an ordinary curve whose automorphism group exceeds the Hurwitz bound.

We give a sharp bound for the automorphism group of a cubic simple graph with a given number of vertices. For each number of vertices we give an explicit graph attaining the bound, and prove its uniqueness in special cases.

We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…

Using a unified method, we determine the structure of automorphisms and representations of arbitrary polyadic groups. More precisely, for a polyadic group $(G, f)=der_{\theta, b}(G, \cdot)$, we obtain a complete description of automorphisms…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…