On 2 - 3 Matrix Chevalley Eilenberg Cohomology
Affiliation(s)
Department of Mathematics and Computer Science, Faculty of Sciences, University of Maroua, Maroua, Cameroon.
Department of Mathematics and Computer Science, Faculty of Sciences, University of Maroua, Maroua, Cameroon.
ABSTRACT
The main objective of this paper is to provide the tool rather than the classical adjoint representation of Lie algebra; which is essential in the conception of the Chevalley Eilenberg Cohomology. We introduce the notion of representation induced by a 2 - 3 matrix. We construct the corresponding Chevalley Eilenberg differential and we compute all its cohomological groups.
The main objective of this paper is to provide the tool rather than the classical adjoint representation of Lie algebra; which is essential in the conception of the Chevalley Eilenberg Cohomology. We introduce the notion of representation induced by a 2 - 3 matrix. We construct the corresponding Chevalley Eilenberg differential and we compute all its cohomological groups.
Cite this paper
Dongho, J. , Duebe-Abi, E. and Yotcha, S. (2015) On 2 - 3 Matrix Chevalley Eilenberg Cohomology. Advances in Pure Mathematics, 5, 835-849. doi: 10.4236/apm.2015.514078.
Dongho, J. , Duebe-Abi, E. and Yotcha, S. (2015) On 2 - 3 Matrix Chevalley Eilenberg Cohomology. Advances in Pure Mathematics, 5, 835-849. doi: 10.4236/apm.2015.514078.
References
[1] Chevalley, C. and Eilenberg, S. (1948) Cohomology Theory of Lie Groups and Lie Algebras. Transactions of the American Mathematical Society, 63, 85-124.
http://dx.doi.org/10.1090/S0002-9947-1948-0024908-8 [2] Nijenhuis, A. and Richardson, R.W. (1967) Deformation of Lie Algebra Structures. Journal of Mathematics and Mechanics, 17, No. 1. [3] Hochschild, G., Kostant, B. and Rosenberg, A. (1962) Differential Forms On Regular Affine Algebras. Transactions of the American Mathematical Society, 102, 383-408.
http://dx.doi.org/10.1090/S0002-9947-1962-0142598-8 [4] Goze, M. (1986) Perturbations of Lie Algebra Structures. In: Hazewinkel, M. and Gerstenhaber, M., Eds., Deformation Theory of Lie Algebra and Structures and Application, NATO ASI Series, Vol. 247, Springer, Netherlands, 265-355. [5] Hefferon, J. (2001) Linear Algebra. Saint Michaels College Colchester, Vermont. [6] Giarlet, P. (1998) Introduction à l’analyse numrique matricielle et l’optimisation. DUMOD.
[1] Chevalley, C. and Eilenberg, S. (1948) Cohomology Theory of Lie Groups and Lie Algebras. Transactions of the American Mathematical Society, 63, 85-124.
http://dx.doi.org/10.1090/S0002-9947-1948-0024908-8 [2] Nijenhuis, A. and Richardson, R.W. (1967) Deformation of Lie Algebra Structures. Journal of Mathematics and Mechanics, 17, No. 1. [3] Hochschild, G., Kostant, B. and Rosenberg, A. (1962) Differential Forms On Regular Affine Algebras. Transactions of the American Mathematical Society, 102, 383-408.
http://dx.doi.org/10.1090/S0002-9947-1962-0142598-8 [4] Goze, M. (1986) Perturbations of Lie Algebra Structures. In: Hazewinkel, M. and Gerstenhaber, M., Eds., Deformation Theory of Lie Algebra and Structures and Application, NATO ASI Series, Vol. 247, Springer, Netherlands, 265-355. [5] Hefferon, J. (2001) Linear Algebra. Saint Michaels College Colchester, Vermont. [6] Giarlet, P. (1998) Introduction à l’analyse numrique matricielle et l’optimisation. DUMOD.