相关论文: The smallest Moufang loop revisited

We determine the minimal polynomial of each element of the double cover $G$ of the symmetric or alternating group in every irreducible spin representation of $G$.

Finite groups are of the greatest importance in science. Loops are a simple generalization of finite groups: they share all the group axioms except for the requirement that the binary operation be associative. The least loops that are not…

The differential equations for a continuous birepresentation of a local analytic Moufang loop are established. The commutation relations for the infinitesimal operators of the representation are found. These commutation relations can be…

A minimal presentation of the cohomology ring of the flag manifold $GL_n/B$ was given in [A. Borel, 1953]. This presentation was extended by [E. Akyildiz-A. Lascoux-P. Pragacz, 1992] to a non-minimal one for all Schubert varieties. Work of…

Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe a randomized algorithm to preprocess the graph in O(gn log n) time…

It is proved that any free Moufang loop can be embedded in a loop of invertible elements of some alternative algebra.

A representation of an object in a category is an abelian group in the corresponding comma category. In this paper we derive the formulas describing linear representations of objects in the category of formal loops and apply them to obtain…

We consider the Euler characteristics $\chi(M)$ of closed orientable topological $2n$-manifolds with $(n-1)$-connected universal cover and a given fundamental group $G$ of type $F_n$. We define $q_{2n}(G)$, a generalized version of the…

Given a weighted, undirected graph $G$ cellularly embedded on a topological surface $S$, we describe algorithms to compute the second shortest and third shortest closed walks of $G$ that are neither homotopically trivial in $S$ nor…

We give presentations, in terms of the generators and relations, for the reflection equation algebras of type $GL_n$ and $SL_n$, i.e., the covariantized algebras of the dual Hopf algebras of the small quantum groups of $\mathfrak{gl}_n$ and…

An A-loop is a loop in which every inner mapping is an automorphism. We settle a problem which had been open since 1956 by showing that every diassociative A-loop is Moufang.

We show that the smallest non-cyclic quotients of braid groups are symmetric groups, proving a conjecture of Margalit. Moreover we recover results of Artin and Lin about the classification of homomorphisms from braid groups on n strands to…

Non-associative finite invertible loops (NAFIL) are loops whose every element has a unique two-sided inverse. Not much is known about the class of NAFIL loops which includes the familiar IP (Inverse Property), Moufang, and Bol loops. Our…

We give a simple construction of new, complete, finite volume manifolds $M$ of bounded, nonpositive curvature. These manifolds have ends that look like a mixture of locally symmetric ends of different ranks and their fundamental groups are…

We initiate (co)homology theory for quasigroups of Bol-Moufang type based on analysis of their extensions by affine quasigroups of the same type. We use these extensions to define second and third boundary operations, $\partial_2(x,y)$ and…

We study homogeneous Lorentzian manifolds $M = G/L$ of a connected reductive Lie group $G$ modulo a connected reductive subgroup $L$, under the assumption that $M$ is (almost) $G$-effective and the isotropy representation is totally…

We describe random loop models and their relations to a family of quantum spin systems on finite graphs. The family includes spin 1/2 Heisenberg models with possibly anisotropic spin interactions and certain spin 1 models with…

An abstract group $G$ is called totally $2$-closed if $H=H^{(2),\Omega}$ for any set $\Omega$ with $G\cong H\leq{\rm Sym}(\Omega)$, where $H^{(2),\Omega}$ is the largest subgroup of ${\rm Sym}(\Omega)$ whose orbits on $\Omega\times\Omega$…

For a finite group $G$, let $m_I(G)$ denote the largest possible cardinality of a minimal invariable generating set of $G$. We prove an upper and a lower bound for $m_I(S_n)$, which show in particular that $m_I(S_n)$ is asymptotic to $n/2$…

The present work is motivated by the statement that the Ising minimal model $\mathcal{M}(4,3)$ is equivalent, at the level of observables, to the $SU(2)_2$ Chern--Simons theory. At first glance, however, these two theories appear to differ…