Related papers: The groupoid structure of groupoid morphisms
The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.
We investigate the double cosets of a groupoid, focusing primarily on their enumeration, by means of two different approaches. The first approach extends the Cauchy-Frobenius lemma to groupoids and interprets it in terms of groupoid…
We construct a description of graded derivations in group algebras. Using this result for arbitrary graduation of the group algebra, we describe all possible structures of DG algebras. The corresponding examples are given. The description…
We describe the automorphism groups of reductive monoids and of root monoids with active groups of invertible elements.
Let us consider a polynomial algebra in three variables equipped with an integer grading. We construct a system of group-generating automorphisms that preserve a given grading.
Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced.It is shown that, given a groupoid $G\rightrightarrows \Omega$ associated with a…
We provide concrete models for generalized morphisms and Morita equivalences of topological 2-groupoids by introducing the notions of crossings and crossed extensions of groupoid crossed modules. A systematic study of these objects is…
In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.
Monoids and groupoids are examples of poloids. On the one hand, poloids can be regarded as one-sorted categories; on the other hand, poloids can be represented by partial magmas of partial transformations. In this article, poloids are…
In this note, we compute the group of automorphisms of Projective, Affine and Euclidean Geometries in the sense of Klein. As an application, we give a simple construction of the outer automorphism of S_6.
This is a biased survey for the Johnson homomorphisms of the automorphism groups of free groups. We just exposit some well known facts and recent developments for the Johnson homomorphisms and its related topics.
In this paper, we extend the classical theory of crossed $G$-sets and the crossed Burnside ring from a finite group $G$ to a finite groupoid $\mathcal{G}$. We introduce a natural monoidal structure on the category of crossed…
We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several…
The group of 2-by-2 matrices with integer entries and determinant $\pm > 1$ can be identified either with the group of outer automorphisms of a rank two free group or with the group of isotopy classes of homeomorphisms of a 2-dimensional…
We compute the automorphism group of OT manifolds of simple type. We show that the graded pieces under a natural filtration are related to a certain ray class group of the underlying number field. This does not solve the open question…
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
We consider rational projective homogeneous varieties over an algebraically closed field of positive characteristic, namely quotients of a semi-simple group by a possibly non-reduced parabolic subgroup. We determine the group scheme…
We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific…
When the theory of Leavitt path algebras was already quite advanced, it was discovered that some of the more difficult questions were susceptible to a new approach using topological groupoids. The main result that makes this possible is…
We show that the holomorph of a cyclic group of order $n$ is isomorphic to its own automophism group when $n$ is twice of a power of an odd prime.