Related papers: Minimal generating sets and the abelianization for…
A generalization of the topological fundamental group is developed in order to exhibit a topologically complete braid group containing Artin's braid group on infinitely many strands with respect to the following notion of convergence: A…
Symplectic and complex toric quasifolds are a generalization of toric manifolds and orbifolds to the nonrational case. In this paper, we reframe these notions from the viewpoint of algebraic geometry.
Fibonacci anyons provide the simplest possible model of non-Abelian fusion rules: [1] x [1] = [0] + [1]. We propose a conformal field theory construction of topological quantum registers based on Fibonacci anyons realized as quasiparticle…
Regular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that…
A lattice-ordered group (an $\ell$-group) $G(\oplus, \vee, \wedge)$ can be naturally viewed as a semiring $G(\vee,\oplus)$. We give a full classification of (abelian) $\ell$-groups which are finitely generated as semirings, by first showing…
The submonoid of the $3$-strand braid group $\mathcal{B}_3$ generated by $\sigma_1$ and $\sigma_1 \sigma_2$ is known to yield an exotic Garside structure on $\mathcal{B}_3$. We introduce and study an infinite family $(M_n)_{n\geq 1}$ of…
Quiver skew braces or skew bracoids are equivalent to braided groupoids, that is, groupoids with a constraint of abelianity. They are the quiver-theoretic version of skew braces, an increasingly studied structure lying in the intersection…
This paper is concerned with the combinatorial description of the graded minimal free resolution of certain monomial algebras which includes toric rings. Concretely, we explicitly describe how the graded minimal free resolution of those…
We generalize the notion of quasielliptic curves, which have infinitesimal symmetries and exist only in characteristic two and three, to a remarkable hierarchy of regular curves having infinitesimal symmetries, defined in all…
Given one of an infinite class of supersymmetric quiver gauge theories, string theorists can associate a corresponding toric variety (which is a Calabi-Yau 3-fold) as well as an associated combinatorial model known as a brane tiling. In…
It has been shown recently that monomial maps in a large class respecting the action of the infinite symmetric group have, up to symmetry, finitely generated kernels. We study the simplest nontrivial family in this class: the maps given by…
We first motivate the study of a certain quotient of the loop braid category, both for the mathematics underpinning recent approaches to topological quantum computation; and as a key example in non-semisimple higher representation theory.…
A minimal (by inclusion) generating set for the algebra of semi-invariants of a quiver of dimension (2,...,2) is established over an infinite field of arbitrary characteristic. The mentioned generating set consists of the determinants of…
We generalize Hrushovski's Group Configuration Theorem to quasiminimal classes. As an application, we present Zariski-like structures, a generalization of Zariski geometries, and show that a group can be found there if the pregeometry…
The phylogenetic semigroup on a graph generalizes the Jukes-Cantor binary model on a tree. Minimal generating sets of phylogenetic semigroups have been described for trivalent trees by Buczy\'nska and Wi\'sniewski, and for trivalent graphs…
We construct a family of links we call torus necklaces for which the link groups are precisely the braid groups of generalised $J$-reflection groups. Moreover, this correspondence exhibits the meridians of the aforementioned link groups as…
Using totally symmetric sets, Chudnovsky, Kordek, Li, and Partin gave a superexponential lower bound on the cardinality of non-abelian finite quotients of the braid group. In this paper, we develop new techniques using multiple totally…
We define pseudo-Garside groups and prove a theorem about them parallel to Garside's result on the word problem for the usual braid groups. The main novelty is that the set of simple elements can be infinite. We introduce a group B=B(Z^n)…
Associated to any closed subgroup $G\subset U_N^+$ is a family of toral subgroups $T_Q\subset G$, indexed by the unitary matrices $Q\in U_N$. The family $\{T_Q|Q\in U_N\}$ is expected to encode the main properties of $G$, and there are…
We introduce in this paper the generalized virtual braid group on n strands GVB_n, generalizing simultaneously the braid groups and their virtual versions. A Mastumoto-Tits type section lifting shuffles in a symmetric group S_n to the…