Baues cofibration for quadratic modules of Lie algebras

Year 2019, Volume: 68 Issue: 2, 1653 - 1663, 01.08.2019

Koray Yılmaz , Elis Soylu Yılmaz

https://doi.org/10.31801/cfsuasmas.468743

Cited By: 2

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.

Keywords

Cofibration Category, Simplicial Lie Algebra, Quadratic Module

References

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