Related papers: On semitopological $\alpha$-bicyclic monoid

Given a finite-dimensional complex simple $\omega$-Lie algebras $\mathfrak{}$ over $\mathbb{C}$. We prove that every local ,$2-$local derivation is a derivation and every local (resp. 2-local) automorphisms are automorphisms or an…

In this thesis we explore natural procedures through which topological structure can be constructed from specific semigroups. We will do this in two ways: 1) we equip the semigroup object itself with a topological structure, and 2) we find…

We prove that Ad-semisimple conjugacy classes in a connected Lie group $G$ are closed embedded submanifolds of $G$. We also prove that if $\alpha:H\to G$ is a homomorphism of connected Lie groups such that the kernel of $\alpha$ is discrete…

In this paper, we study local bifurcations of an indefinite elliptic system with multiple components: \begin{equation*} \left\{\begin{array}{ll} -\Delta u_j + au_j = \mu_ju_j^3+\beta\sum_{k\ne j}u_k^2u_j, u_j>0\ \ \hbox{in}\ \Omega, u_j=0 \…

Let $A$ and $B$ be unital separable simple amenable \CA s which satisfy the Universal Coefficient Theorem. Suppose {that} $A$ and $B$ are $\mathcal Z$-stable and are of rationally tracial rank no more than one. We prove the following:…

We use forcing over admissible sets to show that, for every ordinal $\alpha$ in a club $C\subset\omega_1$, there are copies of $\alpha$ such that the isomorphism between them is not computable in the join of the complete $\Pi^1_1$ set…

In this paper we present general techniques for characterising minimal and maximal semigroup topologies on the endomorphism monoid $\operatorname{End}(\mathbb{A})$ of a countable relational structure $\mathbb{A}$. As applications, we show…

An action of a topological semigroup S on X is compactifiable if this action is a restriction of a jointly continuous action of S on a Hausdorff compact space Y. A topological semigroup S is compactifiable if the left action of S on itself…

We proved the (local) path-connectedness of certain subset of the singular set of semiconcave functions with linear modulus in general. In some sense this result is optimal. The proof is based on a theorem by Marie-Claude Arnaud (M.-C.…

This paper presents a fanctor $S$ from the category of groupoids to the category of semigroups. Indeed, a monoid $S_G$ with a right zero element is related to a topological groupoid $G$. The monoid $S_G$ is a subset of $C(G,G)$, the set of…

We give a complete description of the structure of all bisimple orthodox semigroups generated by two mutually inverse elements.

Given a germ of biholomorphism $F\in\mathrm{Diff}(\mathbb{C}^n,0)$ with a formal invariant curve $\Gamma$ such that the multiplier of the restricted formal diffeomorphism $F|_\Gamma$ is a root of unity or satisfies $|(F|_\Gamma)'(0)|<1$, we…

The aim of this paper is to formulate a local systolic inequality for odd-symplectic forms (also known as Hamiltonian structures) and to establish it in some basic cases. Let $\Omega$ be an odd-symplectic form on an oriented closed manifold…

A monomial algebra B is defined as a quotient of a polynomial ring by a monomial ideal, which is an ideal generated by a finite set of monomials. In this paper, we determine the automorphism group of a monomial algebra B, under the…

Let $k$ be a number field and $B$ be a central simple algebra over $k$ of dimension $p^2$ where $p$ is prime. In the case that $p=2$ we assume that $B$ is not totally definite. In this paper we study sets of pairwise nonisomorphic maximal…

Suppose $G$ is a finite group acting on an Abelian variety $A$ such that the coarse moduli space $A/G$ is smooth. Using the recent classification result due to Auffarth, Lucchini Arteche, and Quezada, we construct an orbifold semiorthogonal…

We show that given a compact minimal system $(X,g)$ and an element $h$ of the topological full group $\tau[g]$ of $g$, then the infinite orbits of $h$ admit a locally constant orientation with respect to the orbits of $g$. We use this to…

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 present some generalizations of the well-known correspondence, found by R. Exel, between partial actions of a group $G$ on a set $X$ and semigroup homomorphism of $S(G)$ on the semigroup $I(X)$ of partial bijections of $X,$ being $S(G)$…

It is known that the canonical double cover of any connected nonbipartite graph have an automorphism group of the form $H \rtimes \mathbb{Z}_2$, where $H$ is the set of automorphism which preserve bipartite parts. We construct connected…