PHD theses : Statistics
Permanent URI for this collectionhttps://repository.neelain.edu.sd/handle/123456789/12106
Browse
2 results
Search Results
Item The Algebraic Treatment of Symmetric Spaces A thesis submitted(Neelain University, 2008) Nemaat Hamed TalebABSTRACT We study manifolds spaces which lead to Lie group, then by definition of transitive action of a Lie group in a manifold we get homogeneous spaces. Also we study symmetric spaces, which are particular homogeneous spaces. We classify simple Lie algebra over C according to Dykin diagram. Also by means of real form we classify simple Lie algebra over DR. We show that every symmetric space gives rise to an orthogonal symmetric Lie algebra. Finally we classify Riemannian symmetric spaces of types I, II, III and IV according to the classification of the irreducible orthogonal symmetric Lie algebra of types I, II, III, and IV.Item The Algebraic Treatment of Symmetric Spaces(Neelain University, 2008) Nemaat Hamed TalebABSTRACT We study manifolds spaces ‘which lead to Lie group, then by definition of transitive action of a Lie group in a manifold we get homogeneous spaces. ' Also we study symmetric spaces, which are particular homogeneous spaces. We classify simple Lie algebra over C according to Dykin diagram. Also by means of real form we classify simple Lie algebra over IR. We show that every symmetric space gives rise to an orthogonal symmetric Lie algebra. Finally we classify Riemannian symmetric spaces of types I, II, III and IV according to the classification of the irreducible orthogonal symmetric Lie algebra of types I, II, III, and IV.