By Boyer Ch. P.
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Additional resources for 3-Sasakian Geometry, Nilpotent Orbits, and Exceptional Quotients
We now want to construct special affine fibrations that correspond to quite general quadratic extensions in the same way as p W T N ! l; Â l ; 0/. l/ \ lC / and Âl0 is induced by Â l . 8. l; Â l / be a proper Z2 -equivariant Lie algebra. l; Â l /-module. g; Â; h ; i/. We assume in addition that at least one of the following two conditions is satisfied: (a) M is simply connected. g/ i? l0 ; Âl0 / and a unique special affine fibration q W M ! N such that dQe D p0 : (6) Here Q is the homomorphism of transvection groups induced by q and p0 is the comp position of natural maps g !
Symmetric powers are symmetric powers of complex vector spaces. Then J induces a real structure on the complex vector spaces S 2k E. l; ˆl /-modules a is trivial. 11. S 4 Hn / . Let l D l D Hn be abelian. S 2 Hn / . bS / and equip aS with the scalar product induced by bS . bS / 2 aS ; v; w 2 Hn : ; aS /. Moreover, ˛S satisfies Condition (T2 ) in Propo; aS / is a hyper-Kähler symmetric triple. It has abelian n 38 I. Kath and M. 4n; 4n/. / D Hn ˚ Hn , ! induced by the dual pairing. Note that Hn E is a Lagrangian subspace, and thus S is a tame solution of (10).
3, admissible cohomology classes correspond to admissible quadratic extensions. l; Âl / be a proper Z2 -equivariant Lie algebra. l; Âl /; a1 / ! l; Âl /; a2 /. l; Â l ; a/] from the right. 3 we arrive at the following classification scheme for symmetric triples. We prefer to formulate it for indecomposable symmetric triples. l; Â l ; a/] . 1 (, Section 6). Let Lp be a complete set of representatives of isomorphism classes of proper Z2 -equivariant Lie algebras. l; Âl / 2 Lp we choose ss . l; Â l ; a/.
3-Sasakian Geometry, Nilpotent Orbits, and Exceptional Quotients by Boyer Ch. P.