The classification of Novikov algebras in low dimensions: invariant bilinear forms

AbstractWe introduce and study ternary f-distributive structures, Ternary f-quandles and more generally their higher n-ary analogues. A classification of ternary f-quandles is provided in low dimensions. Moreover, we study extension theory and introduce a cohomology theory for ternary, and more generally n-ary, f-quandles. Furthermore, we give some computational examples.

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On constructions of Lie (super) algebras and (𝜀,δ)-Freudenthal–Kantor triple systems defined by bilinear forms

Journal of Algebra and Its Applications ◽

10.1142/s0219498820502230 ◽

2019 ◽

Vol 19 (11) ◽

pp. 2050223

Author(s):

Noriaki Kamiya ◽

Daniel Mondoc

Keyword(s):

Lie Algebras ◽

Complex Structure ◽

Bilinear Forms ◽

Simple Lie Algebras ◽

Triple Systems ◽

Dynkin Diagrams

In this work, we discuss a classification of [Formula: see text]-Freudenthal–Kantor triple systems defined by bilinear forms and give all examples of such triple systems. From these results, we may see a construction of some simple Lie algebras or superalgebras associated with their Freudenthal–Kantor triple systems. We also show that we can associate a complex structure into these ([Formula: see text]-Freudenthal–Kantor triple systems. Further, we introduce the concept of Dynkin diagrams associated to such [Formula: see text]-Freudenthal–Kantor triple systems and the corresponding Lie (super) algebra construction.

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NULL HELICES IN LORENTZIAN SPACE FORMS

International Journal of Modern Physics A ◽

10.1142/s0217751x01005821 ◽

2001 ◽

Vol 16 (30) ◽

pp. 4845-4863 ◽

Cited By ~ 55

Author(s):

ANGEL FERRÁNDEZ ◽

ANGEL GIMÉNEZ ◽

PASCUAL LUCAS

Keyword(s):

Minkowski Space ◽

Complete Classification ◽

Space Forms ◽

Lorentzian Space ◽

Low Dimensions ◽

Minkowski Space Time ◽

Minimum Number ◽

Null Curves ◽

Lorentzian Space Forms

In this paper we introduce a reference along a null curve in an n-dimensional Lorentzian space with the minimum number of curvatures. That reference generalizes the reference of Bonnor for null curves in Minkowski space–time and it is called the Cartan frame of the curve. The associated curvature functions are called the Cartan curvatures of the curve. We characterize the null helices (that is, null curves with constant Cartan curvatures) in n-dimensional Lorentzian space forms and we obtain a complete classification of them in low dimensions.

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