Related papers: Acz\'elian n-ary semigroups

Symmetric homology is an analog of cyclic homology in which the cyclic groups are replaced by symmetric groups. The foundations for the theory of symmetric homology of algebras are developed in the context of crossed simplicial groups using…

We introduce and begin to study Lie theoretical analogs of symplectic reflection algebras for a finite cyclic group, which we call "cyclic double affine Lie algebra". We focus on type A : in the finite (resp. affine, double affine) case, we…

We develop some new aspects of cohomology in the context of semi-abelian categories: we establish a Hochschild-Serre 5-term exact sequence extending the classical one for groups and Lie algebras; we prove that an object is perfect if and…

We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…

We show that the continuous \'etale cohomology groups $H^n_{\mathrm{cont}}(X,\mathbf{Z}_l(n))$ of smooth varieties $X$ over a finite field $k$ are spanned as $\mathbf{Z}_l$-modules by the $n$-th Milnor $K$-sheaf locally for the Zariski…

We consider two variants of those Abelian groups with all proper characteristic subgroups isomorphic and give an in-depth study of their basic and specific properties in either parallel or contrast to the Abelian groups with all proper…

Let BS(1,n)= < a,b: aba^{-1}=b^n >. We prove that any finitely-generated group quasi-isometric to BS(1,n) is (up to finite groups) isomorphic to BS(1,n). We also show that any uniform group of quasisimilarities of the real line is…

We begin by introducing schemes of binoids, invertible $\mathcal{O}_M$-sets and cohomology of sheaves of abelian groups defined on schemes of binoids. We define the so-called punctured combinatorial \v{C}ech-Picard complex, whose first…

In 2008, the author proposed a version of duality theory for (not necessarily, Abelian) complex Lie groups, based on the idea of using the Arens-Michael envelope of topological algebra and having an advantage over existing theories in that…

Biserial algebras are a classical class in the representation theory of algebras, generalizing Nakayama algebras. They were further generalized by Green and Schroll to multiserial algebras, which share many structural properties with…

Let $H$ be a monoid (written multiplicatively). We call $H$ Archimedean if, for all $a, b \in H$ such that $b$ is a non-unit, there is an integer $k \ge 1$ with $b^k \in HaH$; strongly Archimedean if, for each $a \in H$, there is an integer…

Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are canonically isomorphic. We discuss how this conjecture can be approached by means of…

It is proved that the additive group of every semidistributive nearring $R$ with an identity is abelian and if R has no elements of order $2$, then the nearring $R$ actually is an associative ring.

Motivated by intuitive properties of physical quantities, the notion of a non-anomalous semigroup is formulated. These are totally ordered semigroups where there are no `infinitesimally close' elements. The real numbers are then defined as…

The algebraic and geometric classifications of complex $3$-dimensional right alternative and semi-alternative algebras are given. As corollaries, we have the algebraic and geometric classification of complex $3$-dimensional…

We study simplicity of $C^*$-algebras arising from self-similar groups of $\mathbb{Z}_2$-multispinal type, a generalization of the Grigorchuk case whose simplicity was first proved by L. Clark, R. Exel, E. Pardo, C. Starling, and A. Sims in…

In 2019, P. Higgins formulated [1] a question about bipartite graphs (see Conjecture 1 below); this question arises in the study of regular finite semigroups. F. V. Petrov formulated [2] another combinatorial conjecture (Conjecture 3);…

We classify the N = 1, 2, 3 superconformal Lie algebras of Schwimmer and Seiberg by means of differential non-abelian cohomology, and describe the general philosophy behind this new technique. The structure of the group (functor) of…

We show that every oriented $n$-dimensional Poincar\'e duality group over a $*$-ring $R$ is amenable or satisfies a linear homological isoperimetric inequality in dimension $n-1$. As an application, we prove the Tits alternative for such…

In the preprint arXiv:2511.07900 we proved that there exists a localizing ring $A_M$ for $A$ an associative ring with unit, and $M=\oplus_{i=1}^rM_i$ a direct sum of $r\geq 1$ simple right $A$-modules. For a homomorphism of associative…