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Forms with O-Orthogonal Lie Algebras

Published online by Cambridge University Press:  20 November 2018

Frank Servedio
Frank Servedio*
Affiliation:
Dept. of Mathematics, William Patterson College, Wayne, New Jersey 07470
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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) =

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 1 , 01 March 1978 , pp. 125 - 126
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Hirzebruch, F., Topological Methods in Algebraic Geometry; Grundlehren Math. Wiss., B. 131, Springer, New York 1966.Google Scholar
2. Borel, A., Linear Algebraic Groups; W. A. Benjamin, Inc., New York 1969.Google Scholar