Related papers: Topologically simple infinite matrix groups indexe…
Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…
Easy quantum groups are compact matrix quantum groups, whose intertwiner spaces are given by the combinatorics of categories of partitions. This class contains the symmetric group and the orthogonal group as well as Wang's quantum…
We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…
Working in the soft-element (classical) viewpoint, we introduce \emph{soft bitopological groups}: soft groups endowed with two soft topologies such that the induced topologies on the set of soft elements make the soft-element group into a…
We give a topological framework for the study of Sela's limit groups: limit groups are limits of free groups in a compact space of marked groups. Many results get a natural interpretation in this setting. The class of limit groups is known…
In this paper, we characterize completely the structure of Clifford semigroups of matrices over an arbitrary field. It is shown that a semigroups of matrices of finite order is a Clifford semigroup if and only if it is isomorphic to a…
We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…
Recently, we have endowed various categories of groups with topologies. The purpose of this paper is to introduce on these categories others topologies which are statistically more suitable to study well-known problems in groups theory. We…
This paper is centered around the classical problem of extracting properties of a finite group $G$ from the ring isomorphism class of its integral group ring $\mathbb{Z} G$. This problem is considered via describing the unit group…
In this article, we introduce an interesting topology-like concept concerning groups (and with almost the same method it can be defined for other algebraic systems). Given an arbitrary group $G$, we define a {\em topo-system} on $G$ as a…
We study groups and rings definable in d-minimal expansions of ordered fields. We generalize to such objects some known results from o-minimality. In particular, we prove that we can endow a definable group with a definable topology making…
We prove that, if $R$ is a non-discrete irreducible, continuous ring, then its unit group $\mathrm{GL}(R)$, equipped with the topology generated by the rank metric, is topologically simple modulo its center, path-connected, locally…
We develop a theory of additive group actions on affine ind-schemes through a purely algebraic and topological framework. Affine ind-schemes are described via complete, second-countable, linearly topologized rings, and actions of the…
Building on the work of Cassels we prove the existence of infinite families of compact orbits of the diagonal group in the space of lattices which accumulate only on the divergent orbit of the standard lattice. As a consequence, we prove…
We construct elementary subgroups of all reductive groups of the local isotropic rank $\geq 2$ over rings and prove their basic properties. In particular, our results may be applied to the automorphism groups of any finitely generated…
Connections between heaps of modules and (affine) modules over rings are explored. This leads to explicit, often constructive, descriptions of some categorical constructions and properties that are implicit in universal algebra and…
We study the topological structure and the topological dynamics of groups of homeomorphisms of scattered spaces. For a large class of them (including the homeomorphism group of any ordinal space or of any locally compact scattered space),…
In this paper we introduce the concept of purely infinite rings, which in the simple case agrees with the already existing notion of pure infiniteness. We establish various permanence properties of this notion, with respect to passage to…
We define the topological complexity sequence of a group as the sequence of topological complexities of its Milnor constructions. This sequence may be regarded as an intrinsic refinement of the topological complexity of a group and, unlike…
The article is devoted to microbundles over topological rings. Their structure, homomorphisms, automorphisms and extensions are studied. Moreover, compactifications and inverse spectra of microbundles over topological rings are…