Related papers: Extensions of groups by weighted Steiner loops

For $G$ a finite group, we show that functions on fields for the 2-dimensional supersymmetric sigma model with background $G$-symmetry determine cocycles for complex analytic $G$-equivariant elliptic cohomology. Similar structures in…

In this paper, we introduce restricted products for families of locally convex spaces and formulate criteria ensuring that mappings into such products are continuous or smooth. As a special case, can define restricted products of weighted…

In [11] we showed that a loop in a simply connected compact Lie group $\dot{U}$ has a unique Birkhoff (or triangular) factorization if and only if the loop has a unique root subgroup factorization (relative to a choice of a reduced sequence…

In the spirit of Glauberman's fundamental work in B-loops and Moufang loops, we prove Cauchy and strong Lagrange theorems for Bol loops of odd order. We also establish necessary conditions for the existence of a simple Bol loop of odd…

Let $\cF$ be a family of finite loops closed under subloops and factor loops. Then every loop in $\cF$ has the strong Lagrange property if and only if every simple loop in $\cF$ has the weak Lagrange property. We exhibit several such…

In this paper we describe how representation theory of groups can be used to shorten the derivation of two loop partition functions in string theory, giving an intrinsic description of modular forms appearing in the results of D'Hoker and…

By a covering of a group G we mean an epimorphism from a group F to G. Introducing the notion of strong covering as a covering pi:F-->G such that every automorphism of G is a projection via pi of an automorphism of F, the main aim of this…

Given a positive weight function and an isometry map on a Hilbert spaces $\mathcal{H}$, we study a class of linear maps which is a $g$-frame, $g$-Riesz basis and a $g$-orthonormal basis for $\mathcal{H}$ with respect to $\mathbb{C}$ in…

This article presents an extended model of gravity obtained by gauging the AdS-Mawell algebra. It involves additional fields that shift the spin connection, leading effectively to theory of two independent connections. Extension of…

In this paper, given a split extension of an arbitrary Coxeter group by automorphisms of the Coxeter graph, we determine the involutions in that extension whose centralizer has finite index. Our result has applications to many problems such…

The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes…

Let $R$ be a discrete valuation ring of field of fractions $K$ and of residue field $k$ of characteristic $p > 0$. In an earlier work, we studied the question of extending torsors on $K$-curves into torsors over $R$-regular models of the…

In this paper we make an attempt to study right loops $(S, o)$ in which, for each $y\in S$, the map $\sigma_y$ from the inner mapping group $G_S$ of $(S, o)$ to itself given by $\sigma_y (h)(x) o\ h(y)= h(xoy)$, $x\in S, h\in G_S$ is a…

We explore gauge fields - strings duality by means of the loop equations and the zigzag symmetry. The results are striking and incomplete. Striking - because we find that the string ansatz proposed in [A.M. Polyakov, hep-th/9711002]…

We study a generalized notion of a homogeneous skew-product extension of a probability-preserving system in which the homogeneous space fibres are allowed to vary over the ergodic decomposition of the base. The construction of such…

We evaluate the robustness and adaptivity of social groups with heterogeneous agents that are characterized by their binary state, their ability to change this state, their status and their preferred relations to other agents. To define…

We show that the automorphism group of a linking system associated to a saturated fusion system $\mathcal{F}$ depends only on $\mathcal{F}$ as long as the object set of the linking system is $\mathrm{Aut}(\mathcal{F})$-invariant. This was…

The strong-coupling character expansion of lattice models is reanalyzed in the perspective of its complete algorithmization. The geometric problem of identifying, counting, and grouping together all possible contributions is disentangled…

We study the structure of abelian extensions of the group $L_qG$ of $q$-differentiable loops (in the Sobolev sense), generalizing from the case of central extension of the smooth loop group. This is motivated by the aim of understanding the…

The anomalous dimensions of planar N=4 SYM theory operators like tr(Phi D^S Phi) expanded in large spin S have the asymptotics \gamma= f ln S + f_c + 1/S (f_11 ln S + f_10) + ..., where f (the universal scaling function or cusp anomaly),…