Related papers: Simple Classes of Automatic Structures

We explore the idea of using automatic and similar kind of presentations of structures to deal with the conceptual problem of natural proof-theoretic ordinal notations. We conclude that this approach still does not meet the goals.

In this paper, we determine the isomorphism classes of the central simple Poisson algebras introduced earlier by the second author. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.

We study certain subgroups of the full group of Hopf algebra automorphisms of a biproduct. In the process interesting subgroups of certain permutation groups come into play.

We obtain a kind of structure theorem for the automorphism group ${\rm Aut}{\cal A}$ of a unital C$^{*}$-algebra ${\cal A}$. According to it, ${\rm Aut}{\cal A}$ can be regarded as a subgroup of the semi-direct product of direct product…

We announce an atlas of subgroup lattices of almost simple groups and present two algorithms that were used to produce the atlas.

The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…

Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two…

We propose a simple approach to formal deformations of associative algebras. It exploits the machinery of multiplicative coresolutions of an associative algebra A in the category of A-bimodules. Specifically, we show that certain…

We consider an amalgam of groups constructed from fusion systems for different odd primes p and q. This amalgam contains a self-normalizing cyclic subgroup of order pq and isolated elements of order p and q.

Classification theory of elementary classes deals with first order (elementary) classes of structures (i.e. fixing a set T of first order sentences, we investigate the class of models of T with the elementary submodel notion). It tries to…

Regular hypermaps with underlying simple hypergraphs are analysed. We obtain an algorithm to classify the regular embeddings of simple hypergraphs with given order, and determine the automorphism groups of regular embedding of simple…

In this paper, we consider a simple class of stratified spaces -- 2-complexes. We present an algorithm that learns the abstract structure of an embedded 2-complex from a point cloud sampled from it. We use tools and inspiration from…

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…

In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some "perfection" property (simpleness, primitiveness, primeness or…

We obtain a complete classification of hypercomplex manifolds, on which a compact group of automorphisms acts transitively. The description of the spaces as well as the proofs of our results use only the structure theory of reductive…

In this paper, the complete algebraic structure of finite semisimple group algebra of a normally monomial group is described. The main result is illustrated by computing the explicit Wedderburn decomposition of finite semisimple group…

We prove structure theorems for the moduli stack of elliptic curves equipped with $G$-structures, where $G$ is a finite 2-generated metabelian group. In particular, we show that if $G$ has exponent $e$, then there is a subgroup $H\le…

Let $k\ge 2$ and let $X$ be a subset of the natural numbers that is $k$-automatic and not eventually periodic. We show that the following dichotomy holds: either all $k$-automatic subsets are definable in the expansion of Presburger…

Automorphism groups of locally finite trees provide a large class of examples of simple totally disconnected locally compact groups. It is desirable to understand the connections between the global and local structure of such a group.…

Regular and higher regular graded algebras (in simplest case satisfying Von Neumann regularity $\Theta_{1}\Theta_{2}\Theta_{1}=\Theta_{1}$ instead of anticommutativity) are introduced and their properties are studied. They are described in…