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Let G and G' be absolutely almost simple algebraic groups of types B and C respectively, of rank at least 3, and defined over a number field K. We determine when G and G' have the same isomorphism or isogeny classes of maximal K-tori. This…
In this paper, we introduce the weakly nilpotent hypergroups with giving some new properties, and then establish several structural characterizations of these hypergroups. Some results obtained in this paper answer the two questions raised…
We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure $M$, Polish group $G$ of permutations of $M$, and $n \geq 1$,…
Connected weakly irreducible not irreducible subgroups of $Sp(1,n+1)\subset SO(4,4n+4)$ that satisfy a certain additional condition are classified. This will be used to classify connected holonomy groups of pseudo-hyper-K\"ahlerian…
We consider (projectively) linearly sofic groups, i.e. groups which can be approximated using (projective) matrices over arbitrary fields, as a generalization of sofic groups. We generalize known results for sofic groups and groups which…
A group $G$ given by a presentation $G = < \mathcal A \| \mathcal R >$ is called weakly finitely presented if every finitely generated subgroup of $G$, generated by (images of) some words in $\mathcal A^{\pm 1}$, is naturally isomorphic to…
We introduce and study soficity for Lie algebras, modelled after linear soficity in associative algebras. We introduce equivalent definitions of soficity, one involving metric ultraproducts and the other involving almost representations. We…
We investigate the weak Hopf algebras of Li based on $U_q[sl_n]$ and Sweedler's finite dimensional example. We give weak Hopf algebra isomorphisms between the weak generalisations of $U_q[sl_n]$ which are ``upgraded'' automorphisms of…
We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…
The weak-strong uniqueness of solutions to a broad class of cross-diffusion systems with volume filling is established. In general, the diffusion matrices are neither symmetric nor positive definite. This issue is overcome by supposing that…
We study injective versions of the characterization of sets potentially in a Wadge class of Borel sets, for the first Borel and Lavrentieff classes. We also study the case of oriented graphs in terms of continuous homomorphisms, injective…
We say that an infinite word w is weak abelian periodic if it can be factorized into finite words with the same frequencies of letters. In the paper we study properties of weak abelian periodicity, its relations with balance and frequency.…
Motivated by the notion of boundary for hyperbolic and $CAT(0)$ groups, M. Bestvina in "Local Homology Properties of Boundaries of Groups" introduced the notion of a (weak) $\mathcal Z$-structure and (weak) $\mathcal Z$-boundary for a group…
We study eigenvalues along periodic cycles of post-critically finite endomorphisms of $\mathbb{CP}^n$ in higher dimension. It is a classical result when $n = 1$ that those values are either $0$ or of modulus strictly bigger than $1$. It has…
The aim of the present paper is to define and study a new class of groups, namely Wm-groups with a single binary operation based on axioms of semi commutativity, right identity and left inverse. Moreover, we introduce the notions of right…
We study a new class of so-called rational-infinitely (or quasi-infinitely) divisible probability laws on the real line. The characteristic functions of these distributions are ratios of the characteristic functions of classical infinitely…
Platonov in 1991 conjectured that adjoint groups are rational as varieties over arbitrary infinite fields, and as a consequence have weak approximation. The rationality part of the conjecture was disproved by Merkurjev in 1996, but the…
Lecture notes on Weak Topologies: We discuss about the weak and weak star topologies on a normed linear space. Our aim is to prove the well known Banach-Alaouglu theorem and discuss some of its consequences, in particular, characterizations…
By computing Frobenius-Schur indicators of modules of certain weak Hopf algebras, we give a formula for the number of involutions in symmetric groups, which are contained in a given coset with respect to a given Young subgroup.
We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…