Related papers: A class of group-like object

It will be shown that Pascal's Theorem is equivalent to the associativity of a natural binary operation on conic sections. A novel proof for Pascal's Theorem will then be given by showing that this binary operation is associative…

In this paper we formalize some foundation concepts and theorems of group theory in a variant of type theory called the Calculus of Constructions with Definitions. In this theory we introduce definition of a group, which is both general and…

In this paper, we classify space-time curves up to Galilean group of transformations with Cartan's method of equivalence. As an aim, we elicit invariats from action of special Galilean group on space-time curves, that are, in fact,…

We introduce the notion of self-similar actions of grouopids on other groupoids and Fell bundles. This leads to a new imprimitivity theorem arising from such dynamics, generalizing many earlier imprimitivity theorems involving group and…

We present a first step towards the Coq implementation of the Theory of Tagged Objects formalism. The concept of tagged types is encoded, and the soundness proofs are discussed with some future work suggestions.

We survey the extensions of a group by a group using crossed products instead of exact sequences of groups. The approach has various advantages, one of them being that the crossed product is an universal object. Several new applications are…

In this paper, we define a new structure analogous to group, called partial group. This structure concerns the partial stability by the composition inner law. We generalize the three isomorphism theorems for groups to partial groups.

We establish some results about large restricted Lie algebras similar to those known in the Group Theory. As an application we use this group-theoretic approach to produce some examples of restricted as well as ordinary Lie algebras which…

We classify representations of compact connected Lie groups whose induced action on the unit sphere has an orbit space isometric to a Riemannian orbifold.

The analogue of Goldie's Theorem for prime rings is proved for rings graded by abelian groups, eliminating unnecessary additional hypotheses used in earlier versions.

Let H be a cocommutative faithfully flat Hopf quasigroup in a strict symmetric monoidal category with equalizers. In this paper we introduce the notion of (strong) Galois H-object and we prove that the set of isomorphism classes of (strong)…

A group is called square-like if it is universally equivalent to its direct square. It is known that the class of all square-like groups admits an explicit first order axiomatization but its theory is undecidable. We prove that the theory…

We generalize the Cauchy-Davenport theorem to locally compact groups.

In the spirit of an earlier result of M\"uller on the Heisenberg group we prove a restriction theorem on a certain class of two step nilpotent Lie groups. Our result extends that of M\"uller also in the framework of the Heisenberg group.

We explain how categories, and groupoids, can be seen as models for a Lawvere ${\mathfrak Gr}$-theory, where ${\mathfrak Gr}$ is the category of graphs, and show that for Lawvere ${\mathfrak Gr}$-theories finitely presentable models are…

A version of Paley-Wiener like theorem for connected, simply connected nilpotent Lie groups is proven.

In this paper using split extensions of group-groupoids we obtain the notion of crossed modules over group-grouoids which are also called 2-groups and we prove a categorical equivalence of these types of crossed modules and double…

We prove a theorem of Tits type about automorphism groups for compact Kahler manifolds, which has been conjectured in the paper [KOZ].

We introduce the notion of the action of a group on a labeled graph and the quotient object, also a labeled graph. We define a skew product labeled graph and use it to prove a version of the Gross-Tucker theorem for labeled graphs. We then…

We define a category parameterizing Calabi-Yau algebra objects in an infinity category of spans. Using this category, we prove that there are equivalences of infinity categories relating, firstly: 2-Segal simplicial objects in C to algebra…