This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.

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.

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...

Higher order generalizations of Lie algebras have equivalently been conceived as Lie n-algebras, as L∞-algebras, or, dually, as quasi-free differential graded commutative algebras. Here we discuss morphisms and higher morphisms of Lie n-algebras, the construction of inner derivation Lie (n+1)-algebras, and the existence of short exact sequences of Lie (2n + 1)-algebras for every transgressive L...

For a perfect Lie algebra h we classify all Lie algebras containing h as a subalgebra of codimension 1. The automorphism groups of such Lie algebras are fully determined as subgroups of the semidirect product h n (k∗ × AutLie(h)). In the non-perfect case the classification of these Lie algebras is a difficult task. Let l(2n + 1, k) be the Lie algebra with the bracket [Ei, G] = Ei, [G,Fi] = Fi, ...

We construct the finite dimensional simple integral modules for the (degenerate) affine Hecke-Clifford algebra (AHCA), H aff Cℓ (d). Our construction includes an analogue of Zelevin-sky's segment representations, a complete combinatorial description of the simple calibrated H aff Cℓ (d)-modules, and a classification of the simple integral H aff Cℓ (d)-modules. Our main tool is an analogue of th...