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Zeitschrift für verallgemeinerte Lügentheorie und -anwendungen

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Volumen 3, Ausgabe 3 (2009)

Forschungsartikel

Bruck decomposition for endomorphisms of quasigroups

Peter T. NAGY and Peter PLAUMANN

In 1944, R. H. Bruck has described a very general construction method which he called the extension of a set by a quasigroup. We use it to construct a class of examples for LF-quasigroups in which the image of the map e(x)=xnx is a group. More generally, we consider the variety of quasigroups which is de ned by the property that the map e is an endomorphism and its subvariety where the image of the map e is a group. We characterize quasigroups belonging to these varieties using their Bruck decomposition with respect to the map e.
Forschungsartikel

On anti-structurable algebras and extended Dynkin diagrams

Noriaki KAMIYA a and Daniel MONDOC

We construct Lie superalgebras osp(2n + 1 j 4n + 2) and osp(2n j 4n) starting with certain classes of anti-structurable algebras via the standard embedding Lie superalgebra construction corresponding to (; )-Freudenthal Kantor triple systems.

Leitartikel

Log-concavity of the cohomology of nilpotent Lie algebras in characteristic two

Grant CAIRNS

It is known that the Betti numbers of the Heisenberg Lie algebras are unimodal over elds of characteristic two. This note observes that they are log-concave. An example is given of a nilpotent Lie algebra in characteristic two for which the Betti numbers are unimodal but not log-concave.

Forschungsartikel

A special form of Rund's h-curvature tensor using R3-like Finsler space

S.T.AVEESH, S.K.NARASIMHAMURTHY, H.G.NAGARAJAb, and Pradeep KUMAR

The purpose of the present paper is to consider and study a special form of Rund's h-curvature tensor Ki ljk and Berwald's curvature tensor Hi ljk in an R3-like C-reducible Finsler space. In this paper, we modify the Rund's h-curvature tensor Ki ljk to special form by using some special Finsler spaces like C-reducible, R3-like Finsler spaces.

Rezensionsartikel

Notes on cohomologies of ternary algebras of associative type

H. ATAGUEMA and A. MAKHLOUF

The aim of this paper is to investigate the cohomologies for ternary algebras of associative type.We study in particular the cases of partially associative ternary algebras and weak totally associative ternary algebras. Also, we consider the Takhtajan's construction, which was used to construct a cohomology of ternary Nambu-Lie algebras using Chevalley-Eilenberg cohomology of Lie algebras, and discuss it in the case of ternary algebras of associative type. One of the main results of this paper states that a usual deformation cohomology does not exist for partially associative ternary algebras which implies that their operad is not a Koszul operad.

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