Related papers: A geometrical characterization of proportionally m…
For an affine spherical homogeneous space G/H of a connected semisimple algebraic group G, we consider the factorization morphism by the action on G/H of a maximal unipotent subgroup of G. We prove that this morphism is equidimensional if…
The R-module functors that are essential for the development of the theory of the linear representations of an affine R-group are the quasi-coherent R-modules and the R-module schemes. The aim of this paper is to study when a quasi-coherent…
The Modular Isomorphism Problem asks if an isomorphism of group algebras of two finite p-groups G and H over a field of characteristic p, implies an isomorhism of the groups G and H. We survey the history of the problem, explain strategies…
Let $A\subset \N_{+}$ and by $P_{A}(n)$ denotes the number of partitions of an integer $n$ into parts from the set $A$. The aim of this paper is to prove several result concerning the existence of integer solutions of Diophantine equations…
The goal of the work is to take on and study one of the fundamental tasks studying Diophantine n-gons (the author of the paper considers an integral n-gon is Diophantine as far as determination of combinatorial properties of each of them…
Functorial semi-norms are semi-normed refinements of functors such as singular (co)homology. We investigate how different types of representability affect the (non-)triviality of finite functorial semi-norms on certain functors or classes.…
For a nondegenerate additive subgroup $G$ of the $n$-dimensional vector space $F^n$ over an algebraically closed field $F$ of characteristic zero, there is an associative algebra and a Lie algebra of Weyl type $W(G,n)$ spanned by all…
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…
Given a finite nonabelian semisimple group $G$, we describe those groups that have the same holomorph as $G$, that is, those regular subgroups $N\simeq G$ of $S(G)$, the group of permutations on the set $G$, such that…
We introduce the notion of pattern for numerical semigroups, which allows us to generalize the definition of Arf numerical semigroups. In this way infinitely many other classes of numerical semigroups are defined giving a classification of…
Given a dense additive subgroup $G$ of $\mathbb R$ containing $\mathbb Z$, we consider its intersection $\mathbb G$ with the interval $[0,1[$ with the induced order and the group structure given by addition modulo $1$. We axiomatize the…
The symmetric inverse semigroup $I(X)$ on a set $X$ is the collection of all partial bijections between subsets of $X$ with composition as the algebraic operation. We study a minimal Hausdorff inverse semigroup topologies on $I(X)$. When…
For homogeneous reductive spaces G/H with reductive complements decomposable into an orthogonal sum \mathfrak{m}=\mathfrak{m}_1 \oplus \mathfrak{m}_2 \oplus \mathfrak{m}_3 of three Ad(H)-invariant irreducible mutually inequivalent…
In this paper, we prove that the numerical-semigroup-gap counting problem is #NP-complete as a main theorem. A numerical semigroup is an additive semigroup over the set of all nonnegative integers. A gap of a numerical semigroup is defined…
In this work, we classify the group gradings on finite-dimensional incidence algebras over a field, where the field has characteristic zero, or the characteristic is greater than the dimension of the algebra, or the grading group is…
A toroidal affine Nash group is the affine Nash group analogue of an anti-affine algebraic group. In this note, we prove analogues of Rosenlicht's structure and decomposition theorems: (1) Every affine Nash group $G$ has a smallest normal…
In this article, we classify all Buchsbaum simplicial affine semigroups whose complement in their (integer) rational polyhedral cone is finite. We show that such a semigroup is Buchsbaum if and only if its set of gaps is equal to its set of…
In this article we study the combinatorics of congruence subgroups of the modular group. We consider the notion of minimal monomial solutions. These are the solutions of a matrix equation (also appearing in the study of Coxeter friezes),…
''Positive geometries'' are a class of semi-algebraic domains which admit a unique ''canonical form'': a logarithmic form whose residues match the boundary structure of the domain. The study of such geometries is motivated by recent…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…