Araştırma Makalesi
BibTex RIS Kaynak Göster

On Simplicial Leibniz Algebras

Yıl 2020, , 1224 - 1232, 01.06.2020
https://doi.org/10.21597/jist.657475

Öz

Aim of this paper is to define simplicial object in category of Leibniz algebras and to show the equivalence between the category of simplicial Leibniz algebras and the category of crossed modules over Leibniz algebras.

Kaynakça

  • Atik M, Aytekin A, Uslu EÖ, 2017. Representability of actions in the category of (Pre)crossed modules in Leibniz algebras. Communications in Algebra, 45(5): 1825–1841.
  • Aytekin A, Casas JM, Uslu EÖ, 2012. Semi-Complete Crossed Modules of Lie Algebras. Journal of Algebra and Its Applications, 11(5): 1–24.
  • Bloh A, 1965. A generalization of the concept of a Lie algebra. Doklady Akademii Lauk, 165 (3): 471–473.
  • Casas JM, 1999. Crossed extensions of Leibniz algebras. Communations in Mathematics, 27 (12): 6253–6272.
  • Casas JM, Fernandez-Casado R, Garcia-Martinez, X, Khmaladze E, 2018. Actor of a Crossed Module of Leibniz Algebras. Theory and Applications of Categories, 33(2): 23–42.
  • Casas JM, Khmaladze E, Ladra M, 2008. Crossed modules for Leibniz n-algebras. Forum Mathematicum, 20: 841–858.
  • D.M. Kan, 1958. A Combinatorial Definition of Homotopy Groups. Annals of Mathematics, 67(2): 288–312.
  • Ellis GJ, 1993. Homotopical aspects of Lie algebras. Journal of The Australian Mathematical Society, 54(3): 393–419.
  • Emir K, Akay HG, Pullback crossed modules in the category of racks. Hacettepe Journal of Mathematics and Statistics, 48(1): 140–149.
  • Loday JL, 1993. Une version non commutative des algebres de Lie: les algebres de Leibniz. L’Enseignement Mathhematique, 39: 269–293.
  • Loday JL, Pirashvili T, 1993. Universal enveloping algebras of Leibniz algebras and (co)homology. Mathematische Annalen, 296(1): 139–158.
  • Şahan T, 2019. Further remarks on liftings of crossed modules. Hacettepe Journal of Mathematics and Statistics, 48(3): 743–752.
  • Şahan T, Erciyes A, 2019. Actions of internal groupoids in the category of Leibniz Algebra. Communications Series A1:Mathematics and Statistics, 68(1): 619–632.
  • Whitehead JHC, 1949. Combinatorial Homotopy. Bulletin of the American Mathematical Society, 55: 453–496.

Simplisel Leibniz Cebirler Üzerine

Yıl 2020, , 1224 - 1232, 01.06.2020
https://doi.org/10.21597/jist.657475

Öz

Bu makalenin temel amacı, Leibniz cebirler kategorisinde simplisel objeyi tanımlayarak, simplisel Leibniz cebirler kategorisi ile Leibniz cebirler üzerinde çaprazlanmış modüller kategorisinin denkliğini göstermektir.

Kaynakça

  • Atik M, Aytekin A, Uslu EÖ, 2017. Representability of actions in the category of (Pre)crossed modules in Leibniz algebras. Communications in Algebra, 45(5): 1825–1841.
  • Aytekin A, Casas JM, Uslu EÖ, 2012. Semi-Complete Crossed Modules of Lie Algebras. Journal of Algebra and Its Applications, 11(5): 1–24.
  • Bloh A, 1965. A generalization of the concept of a Lie algebra. Doklady Akademii Lauk, 165 (3): 471–473.
  • Casas JM, 1999. Crossed extensions of Leibniz algebras. Communations in Mathematics, 27 (12): 6253–6272.
  • Casas JM, Fernandez-Casado R, Garcia-Martinez, X, Khmaladze E, 2018. Actor of a Crossed Module of Leibniz Algebras. Theory and Applications of Categories, 33(2): 23–42.
  • Casas JM, Khmaladze E, Ladra M, 2008. Crossed modules for Leibniz n-algebras. Forum Mathematicum, 20: 841–858.
  • D.M. Kan, 1958. A Combinatorial Definition of Homotopy Groups. Annals of Mathematics, 67(2): 288–312.
  • Ellis GJ, 1993. Homotopical aspects of Lie algebras. Journal of The Australian Mathematical Society, 54(3): 393–419.
  • Emir K, Akay HG, Pullback crossed modules in the category of racks. Hacettepe Journal of Mathematics and Statistics, 48(1): 140–149.
  • Loday JL, 1993. Une version non commutative des algebres de Lie: les algebres de Leibniz. L’Enseignement Mathhematique, 39: 269–293.
  • Loday JL, Pirashvili T, 1993. Universal enveloping algebras of Leibniz algebras and (co)homology. Mathematische Annalen, 296(1): 139–158.
  • Şahan T, 2019. Further remarks on liftings of crossed modules. Hacettepe Journal of Mathematics and Statistics, 48(3): 743–752.
  • Şahan T, Erciyes A, 2019. Actions of internal groupoids in the category of Leibniz Algebra. Communications Series A1:Mathematics and Statistics, 68(1): 619–632.
  • Whitehead JHC, 1949. Combinatorial Homotopy. Bulletin of the American Mathematical Society, 55: 453–496.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Matematik
Bölüm Matematik / Mathematics
Yazarlar

Ali Aytekin 0000-0001-7892-6960

Yayımlanma Tarihi 1 Haziran 2020
Gönderilme Tarihi 10 Aralık 2019
Kabul Tarihi 1 Şubat 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Aytekin, A. (2020). Simplisel Leibniz Cebirler Üzerine. Journal of the Institute of Science and Technology, 10(2), 1224-1232. https://doi.org/10.21597/jist.657475
AMA Aytekin A. Simplisel Leibniz Cebirler Üzerine. Iğdır Üniv. Fen Bil Enst. Der. Haziran 2020;10(2):1224-1232. doi:10.21597/jist.657475
Chicago Aytekin, Ali. “Simplisel Leibniz Cebirler Üzerine”. Journal of the Institute of Science and Technology 10, sy. 2 (Haziran 2020): 1224-32. https://doi.org/10.21597/jist.657475.
EndNote Aytekin A (01 Haziran 2020) Simplisel Leibniz Cebirler Üzerine. Journal of the Institute of Science and Technology 10 2 1224–1232.
IEEE A. Aytekin, “Simplisel Leibniz Cebirler Üzerine”, Iğdır Üniv. Fen Bil Enst. Der., c. 10, sy. 2, ss. 1224–1232, 2020, doi: 10.21597/jist.657475.
ISNAD Aytekin, Ali. “Simplisel Leibniz Cebirler Üzerine”. Journal of the Institute of Science and Technology 10/2 (Haziran 2020), 1224-1232. https://doi.org/10.21597/jist.657475.
JAMA Aytekin A. Simplisel Leibniz Cebirler Üzerine. Iğdır Üniv. Fen Bil Enst. Der. 2020;10:1224–1232.
MLA Aytekin, Ali. “Simplisel Leibniz Cebirler Üzerine”. Journal of the Institute of Science and Technology, c. 10, sy. 2, 2020, ss. 1224-32, doi:10.21597/jist.657475.
Vancouver Aytekin A. Simplisel Leibniz Cebirler Üzerine. Iğdır Üniv. Fen Bil Enst. Der. 2020;10(2):1224-32.