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On Seven-Dimensional Filiform Leibniz Algebras

In: International Conference on Mathematical Sciences and Statistics 2013

Author

Listed:
  • Abdulafeez O. Abdulkareem

    (Universiti Putra Malaysia, Institute for Mathematical Research)

  • I. S. Rakhimov

    (Universiti Putra Malaysia, Department of Mathematics, Faculty of Science)

  • S. K. Said Husain

    (Universiti Putra Malaysia, Department of Mathematics, Faculty of Science)

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.

Suggested Citation

  • Abdulafeez O. Abdulkareem & I. S. Rakhimov & S. K. Said Husain, 2014. "On Seven-Dimensional Filiform Leibniz Algebras," Springer Books, in: Adem Kilicman & Wah June Leong & Zainidin Eshkuvatov (ed.), International Conference on Mathematical Sciences and Statistics 2013, edition 127, pages 1-11, Springer.
    • Handle: RePEc:spr:sprchp:978-981-4585-33-0_1
    DOI: 10.1007/978-981-4585-33-0_1
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