Research ArticleOpen AccessGoogle Scholar indexed
On 2 - 3 Matrix Chevalley Eilenberg Cohomology
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
Department of Mathematics and Computer Science, Faculty of Sciences, University of Maroua, Maroua, Cameroon
- 1 Department of Mathematics and Computer Science, Faculty of Sciences, University of Maroua, Maroua, Cameroon
- 2 Department of Mathematics and Computer Science, Faculty of Sciences, University of Maroua, Maroua, Cameroon
- 3 Department of Mathematics and Computer Science, Faculty of Sciences, University of Maroua, Maroua, Cameroon
Advances in Pure Mathematics·Volume 05 (2015)·Pages 835–849·Published 7 December 2015·DOI10.4236/apm.2015.514078
Copy link · social · email
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.
KeywordsLie AlgebraCochain2 - 3 Matrix Chevalley EilenbergCohomology
- 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
- Nijenhuis, A. and Richardson, R.W. (1967) Deformation of Lie Algebra Structures. Journal of Mathematics and Mechanics, 17, No. 1.
- 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
- 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.
- Hefferon, J. (2001) Linear Algebra. Saint Michaels College Colchester, Vermont.
- Giarlet, P. (1998) Introduction à l’analyse numrique matricielle et l’optimisation. DUMOD.