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

Abstract

The Joseph ideal is a special ideal in the universal enveloping algebra of a simple Lie algebra. For the classical groups, its uniqueness is equivalent to the existence of tensors with special properties.

The existence of these tensors is usually concluded abstractly but here we present explicit formulae. This allows a rather direct computation of a parameter used in defining the Joseph ideal.

Keywords

• Special
• tensors
• deformation
• theory
• quadratic
• algebras
• classical
• algebras