Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Volume: 68 Issue: 2

Baues cofibration for quadratic modules of Lie algebras

Elis Soylu Yılmaz(ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ)0000-0002-0869-310X
Pages
—
Publication Date
2019-08-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We use the free quadratic modules of Lie algebras to show that the category quadratic module of lie algebras is a cofibration category by means of Baues.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper; free quadratic modules and totally free ojects in the category of quadratic modules consructed over Lie algebras.
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Key Findings & Data:In this paper; free quadratic modules and totally free ojects in the category of quadratic modules consructed over Lie algebras.
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Conclusion & Impact:We use the free quadratic modules of Lie algebras to show that the category quadratic module of lie algebras is a cofibration category by means of Baues.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cofibration Category · Simplicial Lie Algebra · Quadratic Module

Abstract

In this paper; free quadratic modules and totally free ojects in the category of quadratic modules consructed over Lie algebras. We use the free quadratic modules of Lie algebras to show that the category quadratic module of lie algebras is a cofibration category by means of Baues.

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Cite This Article

Yılmaz, K., Yılmaz, E. S. (2019). Baues cofibration for quadratic modules of Lie algebras. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 2. https://doi.org/10.31801/cfsuasmas.468743

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References (15)

  1. André, M., Homologie des algébras commutatives, Springer-Verlag, Die Grundlehren der mathematicschen Wissenschaften in Einzeldarstellungen Band, 206, 1974.
  2. Akça, I. and Arvasi, Z., Simplicial and crossed Lie algebras, Homology, Homotopy and Applications, Vol. 4 No.1, (2002),43-57.
  3. Arvasi, Z., 2-crossed complexes and crossed resolutions of Lie algebras, Algebra, Groups and Geometry, Vol. 16,(1999), 452-479.
  4. Baues, H.J., Combinatorial homotopy and 4-dimenional complexes, Walter de Gruyter, 15, 1991.
  5. Carrasco, P. and A.M. Cegarra, Group-theoretic algebraic models for homotopy types, Journal of Pure and Applied Algebra, 75, (1991), 195-235.
  6. Conduché, D., Modules croisés g énéralisés de longueur 2, J. Pure and Applied Algebra, 34, (1984), 155-178.
  7. Curtis, E.B., Simplicial homotopy theory, Adv. in Math., 6, (1971), 107-209.
  8. Ellis, G.J., Homotopical aspects of Lie algebras, J. Austral. Math. Soc. (Series A), 54, (1993), 393-419.
  9. Kan, D.M., A combinatorial definition of homotopy groups, Annals of Maths. 61, (1958), 288-312.
  10. Kassel, C. and Loday, J.L., Extensions centrales d'algébres de Lie, Ann. Inst. Fourier (Grenoble), 33, (1982), 119-142.
  11. Ulualan, E. and Ö. Uslu, E., Quadratic modules for Lie algebras, Hacettepe Journal of Mathematics and Statistics, Vol.40, (3), (2010), 409-419.
  12. Whitehead, J.H.C., Combinatorial Homotopy II, Bull. Amer. Math. Soc., 55, (1949), 453-496.
  13. Akça, I. and Arvasi, Z., Simplicial and crossed Lie algebras, Homology, Homotopy and Applications, Vol. 4 No.1, (2002),43-57.
  14. Conduché, D., Modules croisés g énéralisés de longueur 2, J. Pure and Applied Algebra, 34, (1984), 155-178.
  15. Whitehead, J.H.C., Combinatorial Homotopy II, Bull. Amer. Math. Soc., 55, (1949), 453-496.