Related papers: The structure of idempotent translatable quasigrou…

We show that if a subsemigroup $S$ of the bicyclic monoid ${\mathscr{C}}(p,q)$ contains infinitely many idempotents then $S$ admits only the discrete Hausdorff shift-continuous topology. Also we proof that every right-continuous…

Let G be a finitely presented group, and G' its commutator subgroup. Let C be the Cayley graph of G' with all commutators in G as generators. Then C is large scale simply connected. Furthermore, if G is a torsion-free nonelementary…

Let $K$ be a finite group and let $G$ be a finite group acting on $K$ by automorphisms. In this paper we study two different but intimately related subjects: on the one side we classify all possible multiplicative and associative structures…

The polynomial invariants $q_d$ for a large class of smooth 4-manifolds are shown to satisfy universal relations. The relations reflect the possible genera of embedded surfaces in the 4-manifold and lead to a structure theorem for the…

In this work we show that given a connectivity graph $G$ of a $[[n,k,d]]$ quantum code, there exists $\{K_i\}_i, K_i \subset G$, such that $\sum_i |K_i|\in \Omega(k), \ |K_i| \in \Omega(d)$, and the $K_i$'s are $\tilde{\Omega}(…

Let $X$ be a complex smooth projective variety of dimension $d$. Under some assumption on the cohomology of $X$, we construct mutually orthogonal idempotents in $CH_d(X \times X) \otimes \Q$ whose action on algebraically trivial cycles…

The goal of this article is to investigate nontrivial $m$-quasi-Einstein manifolds globally conformal to an $n$-dimensional Euclidean space. By considering such manifolds, whose conformal factors and potential functions are invariant under…

In this article, we construct infinite families $(G_n)_{n \in \mathbb{N}}$ of finite simple groups $G_n$ of Lie type, such that the rank of $G_n$ strictly increases as $n$ tends to infinity, and such that each $G_n$ is a quotient of the…

We show that the bicategory of (representable) orbifolds and good maps is equivalent to the bicategory of orbifold translation groupoids and generalized equivariant maps. We use this result to define an orbifold version of Bredon…

Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an arbitrary bimodule…

Equivalence relations or, more general, quasiorders (i.e., reflexive and transitive binary relations) $\rho$ have the property that an $n$-ary operation $f$ preserves $\rho$, i.e., $f$ is a polymorphism of $\rho$, if and only if each…

Let $(G,*)$ and $(G',\cdot)$ be groupoids. A bijection $f: G \rightarrow G'$ is called a half-isomorphism if $f(x*y)\in\{f(x)\cdot f(y),f(y)\cdot f(x)\}$, for any $ x, y \in G$. A half-isomorphism of a groupoid onto itself is a…

In this follow-up of the article: Quantum Group of Isometries in Classical and Noncommutative Geometry(arXiv:0704.0041) by Goswami, where quantum isometry group of a noncommutative manifold has been defined, we explicitly compute such…

In this paper, we prove that the ring of polynomial invariants of the Weyl group for an indecomposable and indefinite Kac-Moody Lie algebra is generated by invariant symmetric bilinear form or is trivial depending on $A$ is symmetrizable or…

We show that any group that is hyperbolic relative to virtually nilpotent subgroups, and does not admit peripheral splittings, contains a quasi-isometrically embedded copy of the hyperbolic plane. In natural situations, the specific…

Let $M$ be a cusped finite-volume hyperbolic three-manifold with isometry group $G$. Then $G$ induces a $k$-transitive action by permutation on the cusps of $M$ for some integer $k\ge 0$. Generically $G$ is trivial and $k=0$, but $k>0$ does…

We introduce a new, Kac--Moody-flavoured construction for Lie superalgebras, which incorporates phenomena of the type Q (queer) Lie superalgebra. This is done by replacing a maximal even torus by the most general possible Cartan subalgebra…

Quasifolds are spaces that are locally modelled by quotients of $\mathbb{R}^n$ by countable affine group actions. These spaces first appeared in Elisa Prato's generalization of the Delzant construction, and special cases include leaf spaces…

We prove a number of results having to do with equipping type-I $\mathrm{C}^*$-algebras with compact quantum group structures, the two main ones being that such a compact quantum group is necessarily co-amenable, and that if the…

Two groups are virtually isomorphic if they can be obtained one from the other via a finite number of steps, where each step consists in taking a finite extension or a finite index subgroup (or viceversa). Virtually isomorphic groups are…