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**Extra resources for Algèbre, solutions developpees des exercices, 3eme partie, Les grands theoremes [Algebra]**

**Example text**

With respect to a Cartan subalgebra of Hs and an ordering of its roots, there will be a unique line E ⊂ (C n )∗ spanned by a vector of highest weight. The Hs -orbit F ⊂ P (C n )∗ of E is a minimal Hs -orbit in P (C n )∗ , a generalized flag variety of Hs of some dimension k ≤ n−1, endowed with the hyperplane section bundle L. (In the original case I treated, F is the projectivization of the set of perfect cubes and hence is a P 1 . ) The H-structure B provides identifications TxM ≃ C n unique up to an action of H, so there is a subbundle N ⊂ P(T ∗ M ) whose fiber Nx ⊂ P(T x∗ M ) over x corresponds to F ⊂ P (C n )∗ via any B-identification.

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Schouten - On the number of degrees of freedom of the geodetically moving systems, Proc. Kon. Acad. Wet. Amsterdam 21 (1918), 607–613. ¨ fer - On the classification of holonomy representations, Habili[Schw] L. Schwachho tationsschrift, Universit¨at Leipzig, 1998. [Wi] B. Wilking - On compact Riemannian manifolds with noncompact holonomy groups, 1999 preprint. O. edu 20 S´eminaire BOURBAKI 51`eme ann´ee, 1998-99, no 862 Juin 1999 CLASSICAL COMPUTING, QUANTUM COMPUTING, AND SHOR’S FACTORING ALGORITHM by Yuri I.