Classification of Some Solvable Leibniz Algebras

DEMİR İ., Misra K. C., Stitzinger E.

Algebras and Representation Theory, cilt.19, sa.2, ss.405-417, 2016 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s10468-015-9580-5
  • Dergi Adı: Algebras and Representation Theory
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.405-417
  • Anahtar Kelimeler: Classification, Leibniz algebra, Nilpotency, Solvability
  • Uşak Üniversitesi Adresli: Evet

Özet

Leibniz algebras are certain generalization of Lie algebras. In this paper we give classification of non-Lie solvable (left) Leibniz algebras of dimension ≤ 8 with one dimensional derived subalgebra. We use the canonical forms for the congruence classes of matrices of bilinear forms to obtain our result. Our approach can easily be extended to classify these algebras of higher dimensions. We also revisit the classification of three dimensional non-Lie solvable (left) Leibniz algebras.