Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras

Abstract

Using deformation theory, Braverman and Joseph constructed certain primitive ideals in the enveloping algebras of the simple Lie algebras. Except in the case s l (2, C), there is a special value of the deformation parameter giving an ideal of infinite codimension. For the classical Lie algebras, the uniqueness of the special value is equivalent to the existence of tensors with very particular properties. The existence of these tensors was concluded abstractly by Braverman and Joseph but here we present explicit formulae. This allows a rather direct computation of the special value of the deformation parameter. © 2007 Elsevier Ltd. All rights reserved.