Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2024, Cilt: 36 Sayı: 36, 89 - 100, 12.07.2024
https://doi.org/10.24330/ieja.1446322

Öz

Kaynakça

  • L. Auslander and J. Brezin, Almost algebraic Lie algebras, J. Algebra, 8 (1968), 295-313.
  • Sh. A. Ayupov and B. A. Omirov, On Leibniz algebras, Algebra and operator theory, Tashkent (1997), Kluwer Academic Publishers, (1998), 1-12.
  • Sh. A. Ayupov, B. Omirov and I. Rakhimov, Leibniz Algebras-Structure and Classification, CRC Press, Boca Raton, 2020.
  • D. W. Barnes, Some theorems on Leibniz algebras, Comm. Algebra, 39(7) (2011), 2463-2472.
  • C. Batten, L. Bosko-Dunbar, A. Hedges, J. T. Hird, K. Stagg and E. Stitzinger, A Frattini theory for Leibniz algebras, Comm. Algebra, 41(4) (2013), 1547-1557.
  • J. Feldvoss, Leibniz algebras as non-associative algebras, Nonassociative mathematics and its applications, Contemp. Math., 721 (2019), 115-149.
  • M. Jibladze and T. Pirashvili, Lie theory for symmetric Leibniz algebras, J. Homotopy Relat. Struct., 15(1) (2020), 167-183.
  • S. Siciliano and D. A. Towers, On the subalgebra lattice of a Leibniz algebra, Comm. Algebra, 50(1) (2022), 255-267.
  • E. L. Stitzinger, Frattini subalgebras of a class of solvable Lie algebras, Pacific J. Math., 34 (1970), 177-182.
  • D. A. Towers, A Frattini theory for algebras, Proc. London Math. Soc. (3), 27 (1973), 440-462.
  • D. A. Towers, Solvable Lie $A$-algebras, J. Algebra, 340 (2011), 1-12.
  • D. A. Towers, Leibniz $A$-algebras, Commun. Math., 28(2) (2020), 103-121.
  • D. A. Towers, On the nilradical of a Leibniz algebra, Comm. Algebra, 49(10) (2021), 4345-4347.
  • D. A. Towers and V. R. Varea, Further results on elementary Lie algebras and Lie $A$-algebras, Comm. Algebra, 41(4) (2013), 1432-1441.
  • N. Jacobson, Lie Algebras, Interscience Tracts in Pure and Applied Mathematics, Interscience, New York-London, 1962.

Almost-reductive and almost-algebraic Leibniz algebra

Yıl 2024, Cilt: 36 Sayı: 36, 89 - 100, 12.07.2024
https://doi.org/10.24330/ieja.1446322

Öz

This paper examines whether the concept of an almost-algebraic Lie algebra developed by Auslander and Brezin in
[J. Algebra, 8(1968), 295-313] can be introduced for Leibniz
algebras. Two possible analogues are considered: almost-reductive
and almost-algebraic Leibniz algebras. For Lie algebras these two
concepts are the same, but that is not the case for Leibniz
algebras, the class of almost-algebraic Leibniz algebras strictly
containing that of the almost-reductive ones. Various properties
of these two classes of algebras are obtained, together with some
relationships between $\phi$-free, elementary, $E$-algebras and
$A$-algebras.

Kaynakça

  • L. Auslander and J. Brezin, Almost algebraic Lie algebras, J. Algebra, 8 (1968), 295-313.
  • Sh. A. Ayupov and B. A. Omirov, On Leibniz algebras, Algebra and operator theory, Tashkent (1997), Kluwer Academic Publishers, (1998), 1-12.
  • Sh. A. Ayupov, B. Omirov and I. Rakhimov, Leibniz Algebras-Structure and Classification, CRC Press, Boca Raton, 2020.
  • D. W. Barnes, Some theorems on Leibniz algebras, Comm. Algebra, 39(7) (2011), 2463-2472.
  • C. Batten, L. Bosko-Dunbar, A. Hedges, J. T. Hird, K. Stagg and E. Stitzinger, A Frattini theory for Leibniz algebras, Comm. Algebra, 41(4) (2013), 1547-1557.
  • J. Feldvoss, Leibniz algebras as non-associative algebras, Nonassociative mathematics and its applications, Contemp. Math., 721 (2019), 115-149.
  • M. Jibladze and T. Pirashvili, Lie theory for symmetric Leibniz algebras, J. Homotopy Relat. Struct., 15(1) (2020), 167-183.
  • S. Siciliano and D. A. Towers, On the subalgebra lattice of a Leibniz algebra, Comm. Algebra, 50(1) (2022), 255-267.
  • E. L. Stitzinger, Frattini subalgebras of a class of solvable Lie algebras, Pacific J. Math., 34 (1970), 177-182.
  • D. A. Towers, A Frattini theory for algebras, Proc. London Math. Soc. (3), 27 (1973), 440-462.
  • D. A. Towers, Solvable Lie $A$-algebras, J. Algebra, 340 (2011), 1-12.
  • D. A. Towers, Leibniz $A$-algebras, Commun. Math., 28(2) (2020), 103-121.
  • D. A. Towers, On the nilradical of a Leibniz algebra, Comm. Algebra, 49(10) (2021), 4345-4347.
  • D. A. Towers and V. R. Varea, Further results on elementary Lie algebras and Lie $A$-algebras, Comm. Algebra, 41(4) (2013), 1432-1441.
  • N. Jacobson, Lie Algebras, Interscience Tracts in Pure and Applied Mathematics, Interscience, New York-London, 1962.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebir ve Sayı Teorisi
Bölüm Makaleler
Yazarlar

David A. Towers Bu kişi benim

Erken Görünüm Tarihi 3 Mart 2024
Yayımlanma Tarihi 12 Temmuz 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 36 Sayı: 36

Kaynak Göster

APA Towers, D. A. (2024). Almost-reductive and almost-algebraic Leibniz algebra. International Electronic Journal of Algebra, 36(36), 89-100. https://doi.org/10.24330/ieja.1446322
AMA Towers DA. Almost-reductive and almost-algebraic Leibniz algebra. IEJA. Temmuz 2024;36(36):89-100. doi:10.24330/ieja.1446322
Chicago Towers, David A. “Almost-Reductive and Almost-Algebraic Leibniz Algebra”. International Electronic Journal of Algebra 36, sy. 36 (Temmuz 2024): 89-100. https://doi.org/10.24330/ieja.1446322.
EndNote Towers DA (01 Temmuz 2024) Almost-reductive and almost-algebraic Leibniz algebra. International Electronic Journal of Algebra 36 36 89–100.
IEEE D. A. Towers, “Almost-reductive and almost-algebraic Leibniz algebra”, IEJA, c. 36, sy. 36, ss. 89–100, 2024, doi: 10.24330/ieja.1446322.
ISNAD Towers, David A. “Almost-Reductive and Almost-Algebraic Leibniz Algebra”. International Electronic Journal of Algebra 36/36 (Temmuz 2024), 89-100. https://doi.org/10.24330/ieja.1446322.
JAMA Towers DA. Almost-reductive and almost-algebraic Leibniz algebra. IEJA. 2024;36:89–100.
MLA Towers, David A. “Almost-Reductive and Almost-Algebraic Leibniz Algebra”. International Electronic Journal of Algebra, c. 36, sy. 36, 2024, ss. 89-100, doi:10.24330/ieja.1446322.
Vancouver Towers DA. Almost-reductive and almost-algebraic Leibniz algebra. IEJA. 2024;36(36):89-100.