TL;DR
This paper proves bounds on the weights of graded Lie algebras associated with nondegenerate quadrics, showing that higher weights do not occur beyond certain limits, especially for specific cases like RAQ-quadrics.
Contribution
It establishes new bounds on the weights of graded Lie algebras of automorphisms for nondegenerate quadrics, including special cases such as RAQ-quadrics.
Findings
No nonzero graded components of weight greater than 2k for nondegenerate quadrics of codimension k.
For k=3 and RAQ-quadrics, no components of weight greater than 2.
Bounds on the weights of automorphism Lie algebras for specific classes of quadrics.
Abstract
It is proved that the graded Lie algebras of infinitesimal holomorphic automorphisms of nondegenerate quadric of codimension k do not have nonzero graded components of weight greater than 2k. It is also proved that for and for RAQ-quadrics there are no components of weight greater than 2.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Topics in Algebra · Advanced Algebra and Geometry