On classification of $7$-dimensional odd-nilpotent Leibniz algebras

İsmail Demir

doi:10.15672/hujms.1185538

Araştırma Makalesi

On classification of $7$-dimensional odd-nilpotent Leibniz algebras

Yıl 2024, Cilt: 53 Sayı: 1, 121 - 129, 29.02.2024

İsmail Demir

https://doi.org/10.15672/hujms.1185538

Öz

In this paper we extend the method of canonical form for congruence of bilinear forms to give the classification of some subclasses of $7-$dimensional nilpotent Leibniz algebras. Odd-nilpotent Leibniz algebras are defined as that its even dimensional ideals in lower central series are all zero and the classification of $7-$dimensional complex odd-nilpotent Leibniz algebras with one dimensional Leib ideal is obtained by applying the aforementioned method.

Anahtar Kelimeler

Leibniz algebra, nilpotency, classification

Kaynakça

[1] S. Albeverio, B. A. Omirov and I. S. Rakhimov, Classification of 4-dimensional nilpotent complex Leibniz algebras, Extracta Mathematicae 21(3), 197-210, 2006.
[2] S. A. Ayupov and B. A. Omirov, On 3-dimensional Leibniz algebras, Uzbek. Math. Zh. 1, 9-14, 1999.
[3] A. Bloh, On a generalization of Lie algebra notion, Math. in USSR Doklady 165(3), 471-473, 1965.
[4] J.M. Casas, M.A. Insua, M. Ladra and S. Ladra, An algorithm for the classification of 3-dimensional complex Leibniz algebras, Linear Algebra Appl. 9, 3747-3756, 2012. DOI: 10.1016/j.laa.2011.11.039
[5] I. Demir, K. C. Misra and E. Stitzinger, On classification of four-dimensional nilpotent Leibniz Algebras, Comm. Algebra 45(3), 1012-1018, 2017. DOI: 10.1080/00927872.2016.1172626.
[6] I. Demir, Classification of 5−dimensional complex nilpotent Leibniz algebras, in Representations of Lie Algebras, Quantum Groups and Related Topics, 95-120, Contemp. Math. 713, Amer. Math. Soc., Providence, RI, 2018.
[7] I. Demir, Classification of some subclasses of 6-dimensional nilpotent Leibniz algebras., Turk J. Math. 44, 1925-1940, 2020.
[8] J. L. Loday, Une version non commutative des algebres de Lie: les algebres de Leibniz, Enseign. Math. (2) 39(3-4), 269-293, 1993.
[9] I. M. Rikhsiboev and I. S. Rakhimov, Classification of three dimensional complex Leibniz algebras, AIP Conference Proc. 1450, 358-362, 2012. DOI: 10.1063/1.4724168.
[10] F. D. Teran, Canonical forms for congruence of matrices: a tribute to H. W. Turnbull and A. C. Aitken, 2nd meeting on Linear Algebra, Matrix Analysis and Applications, (ALAMA 2010), Valencia(Spain), 2010.

Yıl 2024, Cilt: 53 Sayı: 1, 121 - 129, 29.02.2024

İsmail Demir

https://doi.org/10.15672/hujms.1185538

Öz

Kaynakça

[1] S. Albeverio, B. A. Omirov and I. S. Rakhimov, Classification of 4-dimensional nilpotent complex Leibniz algebras, Extracta Mathematicae 21(3), 197-210, 2006.
[2] S. A. Ayupov and B. A. Omirov, On 3-dimensional Leibniz algebras, Uzbek. Math. Zh. 1, 9-14, 1999.
[3] A. Bloh, On a generalization of Lie algebra notion, Math. in USSR Doklady 165(3), 471-473, 1965.
[4] J.M. Casas, M.A. Insua, M. Ladra and S. Ladra, An algorithm for the classification of 3-dimensional complex Leibniz algebras, Linear Algebra Appl. 9, 3747-3756, 2012. DOI: 10.1016/j.laa.2011.11.039
[5] I. Demir, K. C. Misra and E. Stitzinger, On classification of four-dimensional nilpotent Leibniz Algebras, Comm. Algebra 45(3), 1012-1018, 2017. DOI: 10.1080/00927872.2016.1172626.
[6] I. Demir, Classification of 5−dimensional complex nilpotent Leibniz algebras, in Representations of Lie Algebras, Quantum Groups and Related Topics, 95-120, Contemp. Math. 713, Amer. Math. Soc., Providence, RI, 2018.
[7] I. Demir, Classification of some subclasses of 6-dimensional nilpotent Leibniz algebras., Turk J. Math. 44, 1925-1940, 2020.
[8] J. L. Loday, Une version non commutative des algebres de Lie: les algebres de Leibniz, Enseign. Math. (2) 39(3-4), 269-293, 1993.
[9] I. M. Rikhsiboev and I. S. Rakhimov, Classification of three dimensional complex Leibniz algebras, AIP Conference Proc. 1450, 358-362, 2012. DOI: 10.1063/1.4724168.
[10] F. D. Teran, Canonical forms for congruence of matrices: a tribute to H. W. Turnbull and A. C. Aitken, 2nd meeting on Linear Algebra, Matrix Analysis and Applications, (ALAMA 2010), Valencia(Spain), 2010.

Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Matematik
Yazarlar	İsmail Demir 0000-0002-8070-6489
Erken Görünüm Tarihi	15 Ağustos 2023
Yayımlanma Tarihi	29 Şubat 2024
Yayımlandığı Sayı	Yıl 2024 Cilt: 53 Sayı: 1

Kaynak Göster

APA	Demir, İ. (2024). On classification of $7$-dimensional odd-nilpotent Leibniz algebras. Hacettepe Journal of Mathematics and Statistics, 53(1), 121-129. https://doi.org/10.15672/hujms.1185538
AMA	Demir İ. On classification of $7$-dimensional odd-nilpotent Leibniz algebras. Hacettepe Journal of Mathematics and Statistics. Şubat 2024;53(1):121-129. doi:10.15672/hujms.1185538
Chicago	Demir, İsmail. “On Classification of $7$-Dimensional Odd-Nilpotent Leibniz Algebras”. Hacettepe Journal of Mathematics and Statistics 53, sy. 1 (Şubat 2024): 121-29. https://doi.org/10.15672/hujms.1185538.
EndNote	Demir İ (01 Şubat 2024) On classification of $7$-dimensional odd-nilpotent Leibniz algebras. Hacettepe Journal of Mathematics and Statistics 53 1 121–129.
IEEE	İ. Demir, “On classification of $7$-dimensional odd-nilpotent Leibniz algebras”, Hacettepe Journal of Mathematics and Statistics, c. 53, sy. 1, ss. 121–129, 2024, doi: 10.15672/hujms.1185538.
ISNAD	Demir, İsmail. “On Classification of $7$-Dimensional Odd-Nilpotent Leibniz Algebras”. Hacettepe Journal of Mathematics and Statistics 53/1 (Şubat 2024), 121-129. https://doi.org/10.15672/hujms.1185538.
JAMA	Demir İ. On classification of $7$-dimensional odd-nilpotent Leibniz algebras. Hacettepe Journal of Mathematics and Statistics. 2024;53:121–129.
MLA	Demir, İsmail. “On Classification of $7$-Dimensional Odd-Nilpotent Leibniz Algebras”. Hacettepe Journal of Mathematics and Statistics, c. 53, sy. 1, 2024, ss. 121-9, doi:10.15672/hujms.1185538.
Vancouver	Demir İ. On classification of $7$-dimensional odd-nilpotent Leibniz algebras. Hacettepe Journal of Mathematics and Statistics. 2024;53(1):121-9.