XModLie Fibred Over Lie Algebras

Abstract

In this work, we showed that the category of crossed modules over Lie algebras is fibred over the category of Lie algebras by illustrating that the forgetful functor is a fibration.

Keywords

• pullback
• fibration
• Lie algebras
• crossed modules

References

1. Akca,_I. and Arvasi, Z. Simplicial and Crossed Lie Algebras, homology, Homotopy and Applications, 4 (2002), 43-57.
2. Gerstenhaber, M. On the deformation of Rings and Algebras, Ann. math, no. 84, (1966), 16.
3. Kassel, C. and Loday, J. L. Extensions centrales d'algbres de Lie Ann. Inst. Fourier, Grenoble (1982), 32: 119-142.
4. Lavendhomme, R. and Roisin, J.R. Cohomologie non abelienne de structures alge- briques, J.Algebra 99 (2), (1980), 385-414.
5. Lichtenbaum, S. and Schlessingger, M. The contangent complex of a morphism, Trans. American Society, no. 18, (1967), pp. 41-70.
6. Mosseri, R. and Dandolo, R. Geometry of entangled states, Bloch spheres and Hopf brations., J. Phys. A, 34 (2001), 10243-10252.
7. Porter, T., Homology of Commutative Algebras and an Invariant of Simis and Vas- conceles, J.Algebra 99, (1986), 458-465.
8. Porter, T., Crossed modules and internal categories of groups with operations, Proc. Edinburgh Math. Soc., (2) 30, (1987), no:3, 373-381.

9. Samelson, H., Notes on Lie Algebra, University of Crete Department of Mathematics, 165 (1969), 1-3.
10. Shammu, N.M., Algebraic and Categorical Structure of Category of Crossed Modules of Algebras, Ph.D, U C N W., (1992).
11. Whitehead, J.H.C., Combinatorial Homotopy II , Bull.American Math. Society, 55 (1949), 453-456.