Research Article

Homotopies of Crossed Modules of Lie Algebras

Volume: 6 Number: 2 October 15, 2018
EN

Homotopies of Crossed Modules of Lie Algebras

Abstract

In this paper we will define a notion of homotopy of Lie crossed module morphisms. Then we construct a groupoid structure of Lie crossed module morphisms and their homotopies.



Keywords

References

  1. [1] AKCA, I.I. - EMIR, K. - MARTINS, J.F. Pointed Homotopy of Between 2-Crossed Modules of Commutative Algebras, Homology, Homotopy and Applications vol.17(2) pages 1-30, (2015).
  2. [2] BROWN, R. AND HIGGINS P. J., Tensor Products and Homotopies for w􀀀groupoids and crossed complexes, Journal of Pure and Applied Algebra 47, (1987), 1-33.
  3. [3] CABELLO, J.G. AND GARZON A.R. Closed model structures for algebraic models of n-types, Journal of Pure and Applied Algebra 103 (3), (1995), 287–302.
  4. [4] DWYER, W.G. - SPALINSKI, J. Homotopy theories and model categories, In Handbook of algebraic topology, pages 73-126. Amsterdam: Nort Holland, (1995)
  5. [5] GOHLA, B. - MARTINS, J.F. Pointed Homotopy and Pointed Lax Homotopy of 2-Crossed Module Maps, Adv. Math. 248: pages 986-1049, (2013).
  6. [6] KASEL, C. and LODAY, J.L. Extensions centrales d’algebres de Lie. Ann. Inst. Fourier (Grenoble), 33, (1982) 119-142.
  7. [7] NOOHI, B. Notes on 2-groupoids, 2-groups and crossed modules, Homology Homotopy Appl. 9 (1), (2007), 75-106.
  8. [8] WHITEHEAD, J.H.C. Combinatorial Homotopy I and II, Bull. Amer. Math. Soc., 55, 231-245 and 453-456 (1949).

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Yavuz Sidal This is me

Publication Date

October 15, 2018

Submission Date

February 14, 2018

Acceptance Date

October 3, 2018

Published in Issue

Year 2018 Volume: 6 Number: 2

APA
Akça, İ. İ., & Sidal, Y. (2018). Homotopies of Crossed Modules of Lie Algebras. Konuralp Journal of Mathematics, 6(2), 259-263. https://izlik.org/JA37YA92PD
AMA
1.Akça İİ, Sidal Y. Homotopies of Crossed Modules of Lie Algebras. Konuralp J. Math. 2018;6(2):259-263. https://izlik.org/JA37YA92PD
Chicago
Akça, İbrahim İlker, and Yavuz Sidal. 2018. “Homotopies of Crossed Modules of Lie Algebras”. Konuralp Journal of Mathematics 6 (2): 259-63. https://izlik.org/JA37YA92PD.
EndNote
Akça İİ, Sidal Y (October 1, 2018) Homotopies of Crossed Modules of Lie Algebras. Konuralp Journal of Mathematics 6 2 259–263.
IEEE
[1]İ. İ. Akça and Y. Sidal, “Homotopies of Crossed Modules of Lie Algebras”, Konuralp J. Math., vol. 6, no. 2, pp. 259–263, Oct. 2018, [Online]. Available: https://izlik.org/JA37YA92PD
ISNAD
Akça, İbrahim İlker - Sidal, Yavuz. “Homotopies of Crossed Modules of Lie Algebras”. Konuralp Journal of Mathematics 6/2 (October 1, 2018): 259-263. https://izlik.org/JA37YA92PD.
JAMA
1.Akça İİ, Sidal Y. Homotopies of Crossed Modules of Lie Algebras. Konuralp J. Math. 2018;6:259–263.
MLA
Akça, İbrahim İlker, and Yavuz Sidal. “Homotopies of Crossed Modules of Lie Algebras”. Konuralp Journal of Mathematics, vol. 6, no. 2, Oct. 2018, pp. 259-63, https://izlik.org/JA37YA92PD.
Vancouver
1.İbrahim İlker Akça, Yavuz Sidal. Homotopies of Crossed Modules of Lie Algebras. Konuralp J. Math. [Internet]. 2018 Oct. 1;6(2):259-63. Available from: https://izlik.org/JA37YA92PD
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