Geodesic
Forms with O-Orthogonal Lie Algebras
Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 125-126

Voir la notice de l'article provenant de la source Cambridge University Press

A form P of degree r is a homogeneous polynomial in k[Yi , ..., Yn] on kn, k a field; Yi are the coordinate functions on kn. Let V(n, r) denote the k-vector space of forms of degree r. Mn(k) = Endk(kn) has canonical Lie algebra structure with [A, B] = AB-BA and it acts as a k-Lie Algebra of kderivations of degree 0 on k[Yi , ..., Yn] defined by setting D(A)Y= Yo(-A) for A∈Endk(kn), Y∈V(n,l) = Homk(kn, k) and extending as a k-derivation. Define the orthogonal Lie Algebra, LO(P), of P by LO(P) = 
Servedio, Frank. Forms with O-Orthogonal Lie Algebras. Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 125-126. doi: 10.4153/CMB-1978-022-2
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