相关论文: Dehornoy-like left orderings and isolated left ord…

We prove that the order of an ordered group is an interval order if and only if it is a semiorder. Next, we prove that every semiorder is isomorphic to a collection $\mathcal J$ of intervals of some totally ordered abelian group, these…

In this paper we consider the $f$-orthomorphisms and $f$-linear operators on the order dual of an $f$-algebra. In particular, when the $f$-algebra has the factorization property (not necessarily unital), we prove that the orthomorphisms,…

We show that if a nontrivial group admits a locally invariant ordering, then it admits uncountably many locally invariant orderings. For the case of a left-orderable group, we provide an explicit construction of uncountable families of…

We study P-groupoids that arise from certain decompositions of complete graphs. We show that left distributive P-groupoids are distributive, quasigroups. We characterize P-groupoids when the corresponding decomposition is a Hamiltonian…

We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…

We answer a question of Downey and Kurtz on left-orderable groups by showing that there is a computable left-orderable group which is not classically isomorphic to a computable group with a computable left-order.

We give an algebraic characterisation of ordered groupoids, namely, we show that there is a categorical isomophism between the category of ordered groupoids and the category of $D$-inverse constellations. Here constellations are partial…

A non-trivial element of a group is a generalized torsion element if some products of its conjugates is the identity. The minimum number of such conjugates is called a generalized torsion order. We provide several restrictions for…

In connection with the emerging theory of Garside categories, we develop the notions of a left-Garside category and of a locally left-Garside monoid. In this framework, the connection between the self-distributivity law LD and braids…

Right feeble groups are defined as groupoids $(X,*)$ such that (i) $x, y\in X$ implies the existence of $a, b \in X$ such that $a*x = y$ and $b*y = x$. Furthermore, (ii) if $x, y, z \in X$ then there is an element $w\in X$ such that…

We describe new types of normal forms for braid monoids, Artin-Tits monoids, and, more generally, for all monoids in which divisibility has some convenient lattice properties (``locally Garside monoids''). We show that, in the case of…

Let G be a countable group. We show there is a topological relationship between the space CO(G) of circular orders on G and the moduli space of actions of G on the circle; as well as an analogous relationship for spaces of left orders and…

We give many examples of algebraic actions which are factors of Bernoulli shifts. These include certain harmonic models over left orderable groups of large enough growth, as well as algebraic actions associated to certain lopsided elements…

We propose a new unified framework for Thompson-like groups using a well-known device called operads and category theory as language. We discuss examples of operad groups which have appeared in the literature before. As a first application,…

Using fiber products, we construct bi-orderable groups from left-orderable groups. As an application, we show that bi-orderability is not a profinite property, answering a question of Piwek and Wykowski negatively. We also show that the…

There are various results that frame left-orderability of a group as a geometric property. Indeed, the fundamental group of a 3-manifold is left-orderable whenever the first Betti number is positive; in the case that the first Betti number…

We describe a procedure for constructing a generalized Thompson group out of a family of groups that is equipped with what we call a cloning system. The previously known Thompson groups F, V, Vbr and Fbr arise from this procedure using,…

Let $G$ be the group of all order-preserving self-maps of the real line. In previous work, the first two authors constructed a pre-Tannakian category $\underline{\mathrm{Rep}}(G)$ associated to $G$. The present paper is a detailed study of…

We study Dirichlet forms and Laplacians on self-similar sets with overlaps. A notion of "finitely ramified of finite type($f.r.f.t.$) nested structure" for self-similar sets is introduced. It allows us to reconstruct a class of self-similar…

We describe a simple scheme for constructing finitely generated monoids in which left-divisibility is a linear ordering and for practically investigating these monoids. The approach is based on subword reversing, a general method of…