6 Lie Derivatives and the Commutator Revisited 21 6.1 Integral Curves . . . . . . . . . . . . . . . . . . . . . . . . . . 21 6.2 Congruence of Curves . . . . . . . . . . . . . . . . . . . . . . . 21 6.3 The Commutator Revisited: A Geometric Interpretation . . . 22 6.4 Lie Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . 24 6.5 Lie Derivatives of a Function . . . . . . . . . . . ....

After dimensional reduction to three dimensions, the lowest order effective actions for pure gravity, M-theory and the Bosonic string admit an enhanced symmetry group. In this paper we initiate study of how this enhancement is affected by the inclusion of higher derivative terms. In particular we show that the coefficients of the scalar fields associated to the Cartan subalgebra are given by we...

This paper illustrates the notion of a Cartan subalgebra in a C*algebra through a number of examples and counterexamples. Some of these examples have a geometrical flavour and are related to orbifolds and nonHausdorff manifolds.

In this paper we study the notion of strong non-reflection, and its contrapositive weak reflection. We say θ strongly non-reflects at λ iff there is a function F : θ −→ λ such that for all α < θ with cf(α) = λ there is C club in α such that F 1 C is strictly increasing. We prove that it is consistent to have a cardinal θ such that strong non-reflection and weak reflection each hold on an unboun...

where Δpu = div(|∇u|p−2∇u) is the p-Laplacian of u with 1 < p < ∞, and λ is a real parameter. Moreover, Ω is a smooth bounded domain in RN , N ≥ 1, whose boundary ∂Ω is made of two disjoint nonempty closed sets Γ1 and Γ2 which are smooth manifolds of dimension N − 1, m and n are weights which may be indefinite and unbounded, ∂/∂ν denotes the exterior normal derivative, and u± = max{±u,0}. The m...

Recently, V.Ginzburg introduced the notion of a principal nilpotent pair (= pn-pair) in a semisimple Lie algebra g [Gi99]. It is a double counterpart of the notion of a regular nilpotent element in g. A pair e = (e1, e2) ∈ g × g is called nilpotent, if [e1, e2] = 0 and there exists a pair h = (h1, h2) of semisimple elements such that [h1, h2] = 0, [hi, ej ] = δijej (i, j ∈ {1, 2}). A pn-pair e ...

We consider the supercircle S equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on S as the Lie superalgebra of contact vector fields; it contains the Möbius superalgebra osp(1|2). We study the space of linear differential operators on weighted densities as a module over osp(1|2). We introduce the canonical isomorphism between this space and the correspondin...

The purpose of this paper is to study Hom-Lie superalgebras, that is a superspace with a bracket for which the superJacobi identity is twisted by a homomorphism. This class is a particular case of Γ-graded quasi-Lie algebras introduced by Larsson and Silvestrov. In this paper, we characterize Hom-Lie admissible superalgebras and provide a construction theorem from which we derive a one paramete...

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

We study roles of quark-quark correlations in the baryons for the deep inelastic structure function and the I = 1=2 rule of the non-leptonic weak hyperon decay. The quark-quark correlation is incorporated phenomenologically as diquarks within the Nambu and Jona-Lasinio model. The strong diquark correlations in the spin-0 channel enhance the I = 1=2 weak matrix elements, and account for the I = ...