Related papers: The Isomorphism Problem for Computable Abelian p-G…

For a class of pointed Hopf algebras including the quantized enveloping algebras, we discuss cleft extensions, cocycle deformations and the second cohomology. We present such a non-standard method of computing the abelian second cohomology…

This paper establishes the separation of complexity classes $\mathbf{P}$ and $\mathbf{NP}$ through a novel homological algebraic approach grounded in category theory. We construct the computational category $\mathbf{Comp}$, embedding…

In this paper we study structural properties of LV-degrees of the algebra of collections of sequences that are non-negligible in the sense that they can be computed by a probabilistic algorithm with positive probability. We construct atoms…

The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions…

Let G be a finitely presented group, and let p be a prime. Then G is 'large' (respectively, 'p-large') if some normal subgroup with finite index (respectively, index a power of p) admits a non-abelian free quotient. This paper provides a…

The word problem for discrete groups is well-known to be undecidable by a Turing Machine; more precisely, it is reducible both to and from and thus equivalent to the discrete Halting Problem. The present work introduces and studies a real…

We obtain some new results on the topology of unary definable sets in densely ordered Abelian groups of burden groups of burden 2. In the special case in which the structure has dp-rank 2, we show that the existence of an infinite definable…

This article is dedicated to the computation of an explicit presentation of some asymptotically rigid mapping class groups, namely the braided Higman-Thompson groups. To do so, we use the action of these groups on the spine complex, a…

We provide an algebraic characterization of strong ordered Abelian groups: An ordered Abelian group is strong iff it has bounded regular rank and almost finite dimension. Moreover, we show that any strong ordered Abelian group has finite…

We count the number of isomorphism classes of degree $d$-twists of some polarized abelian varieties over finite fields of odd prime dimension. This can be seen as a higher dimensional analogue of the counting problem for elliptic curves…

We consider the problem of characterizing isomorphisms of types, or, equivalently, constructive cardinality of sets, in the simultaneous presence of disjoint unions, Cartesian products, and exponentials. Mostly relying on results about…

Cameron, Manna and Mehatari investigated the question of which finite groups admit a power graph that is a cograph, also called power-cograph groups (Journal of Algebra 591 (2022)). They give a classification for nilpotent groups and…

We study the local isomorphism classes, also known as genera or weak equivalence classes, of fractional ideals of orders in \'etale algebras. We provide a classification in terms of linear algebra objects over residue fields. As a…

We extend the loop algebra construction for algebras graded by abelian groups to study graded-simple algebras over the field of real numbers (or any real closed field). As an application, we classify up to isomorphism the graded-simple…

A topological group G is profinite if it is compact and totally disconnected. Equivalently, G is the inverse limit of a surjective system of finite groups carrying the discrete topology. We discuss how to represent a countably based…

Any non-abelian finite $p$-group has a non-inner automorphism of order $p$.

We consider three (2-)categories and their (anti-)equivalence. They are the category of small abelian categories and exact functors, the category of definable additive categories and interpretation functors, the category of locally coherent…

In this paper, we study the isomorphism problem for central extensions. More precisely, in some new situations, we provide necessary and sufficient conditions for two central extensions to be isomorphic. We investigate the case when the…

Suppose $p \geq 1$ is a computable real. We extend previous work of Clanin, Stull, and McNicholl by classifying the computable $L^p$ spaces whose underlying measure spaces are atomic but not purely atomic. In addition, we determine the…

Let $p$ be a nonzero complex number. Recently, a class of infinite rank Lie conformal algebras $\mathfrak{B}(p)$ was introduced in [13]. In this paper, we study the structure theory of this class of Lie conformal algebras. Specifically, we…