Abstract
This paper gives complete classification of a subclass of seven-dimensional complex filiform Leibniz algebras denoted by TLb n in fixed dimension n. The classification is carried out by choosing a basis which is adapted. Through this basis, an appropriate table of multiplication of the algebra is constructed. This leads to establishment of necessary and sufficient condition for any two algebras to be isomorphic. According to this condition, we break this class into 30 subsets and as a result, 10 of these subsets are single orbits and the remaining are union of parametric family of orbits. The single orbits are outlined from the parametric ones and their respective representatives are given. In parametric orbits case, the invariants that characterize the parameter are given. The filiform Lie algebras in this dimension are pointed out.
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Acknowledgement
This research was supported by the Universiti Putra Malaysia (UPM) through the research grant 05-02-12-2188RU.
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Abdulkareem, A., Rakhimov, I., Said Husain, S. (2014). On Seven-Dimensional Filiform Leibniz Algebras. In: Kilicman, A., Leong, W., Eshkuvatov, Z. (eds) International Conference on Mathematical Sciences and Statistics 2013. Springer, Singapore. https://doi.org/10.1007/978-981-4585-33-0_1
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DOI: https://doi.org/10.1007/978-981-4585-33-0_1
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