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Homotopies of Crossed Modules of Lie Algebras

Year 2018, Volume: 6 Issue: 2, 259 - 263, 15.10.2018

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.



References

  • [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] 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] 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] DWYER, W.G. - SPALINSKI, J. Homotopy theories and model categories, In Handbook of algebraic topology, pages 73-126. Amsterdam: Nort Holland, (1995)
  • [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] KASEL, C. and LODAY, J.L. Extensions centrales d’algebres de Lie. Ann. Inst. Fourier (Grenoble), 33, (1982) 119-142.
  • [7] NOOHI, B. Notes on 2-groupoids, 2-groups and crossed modules, Homology Homotopy Appl. 9 (1), (2007), 75-106.
  • [8] WHITEHEAD, J.H.C. Combinatorial Homotopy I and II, Bull. Amer. Math. Soc., 55, 231-245 and 453-456 (1949).
Year 2018, Volume: 6 Issue: 2, 259 - 263, 15.10.2018

Abstract

References

  • [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] 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] 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] DWYER, W.G. - SPALINSKI, J. Homotopy theories and model categories, In Handbook of algebraic topology, pages 73-126. Amsterdam: Nort Holland, (1995)
  • [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] KASEL, C. and LODAY, J.L. Extensions centrales d’algebres de Lie. Ann. Inst. Fourier (Grenoble), 33, (1982) 119-142.
  • [7] NOOHI, B. Notes on 2-groupoids, 2-groups and crossed modules, Homology Homotopy Appl. 9 (1), (2007), 75-106.
  • [8] WHITEHEAD, J.H.C. Combinatorial Homotopy I and II, Bull. Amer. Math. Soc., 55, 231-245 and 453-456 (1949).
There are 8 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

İbrahim İlker Akça

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 Issue: 2

Cite

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