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The Description of Orbits Under an Action of GL 9 ON SLb 9

In: International Conference on Mathematical Sciences and Statistics 2013

Author

Listed:
  • I. S. Rakhimov

    (Universiti Putra Malaysia, Laboratory of Cryptography, Analysis and Structure, (INSPEM) & Department of Mathematics, Faculty of Science)

  • S. K. Said Husain

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

  • F. Deraman

    (Universiti Putra Malaysia, Institute for Mathematical Research)

Abstract

The paper concerns with the classification problem of a subclass of nine-dimensional complex filiform Leibniz algebras. The concepts of adapted basis and adapted transformations are given to express the action (“transport of structure”) of the adapted transformations group on SLb 9. We present SLb 9 as a disjoint union of its subsets and specify the orbits under the action of adapted transformations. The list of isomorphism classes of SLb 9 with their representatives and the table of multiplications are given.

Suggested Citation

  • I. S. Rakhimov & S. K. Said Husain & F. Deraman, 2014. "The Description of Orbits Under an Action of GL 9 ON SLb 9," Springer Books, in: Adem Kilicman & Wah June Leong & Zainidin Eshkuvatov (ed.), International Conference on Mathematical Sciences and Statistics 2013, edition 127, pages 139-153, Springer.
    • Handle: RePEc:spr:sprchp:978-981-4585-33-0_15
    DOI: 10.1007/978-981-4585-33-0_15
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