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|Title:||The Algebraic Treatment of Symmetric Spaces A thesis submitted|
|Authors:||Nemaat Hamed Taleb|
|Abstract:||ABSTRACT 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.|
|Description:||A thesis submitted for the degree of Ph. D. in Mathematics|
|Appears in Collections:||PHD theses : Statistics|
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