Deformations of quadratic algebras, the Joseph ideal for classical Lie algebras, and special tensors
2007
Abstract
The Joseph ideal is a unique ideal in the universal enveloping algebra of a simple Lie algebra attached to the minimal coadjoint orbit. Its construction using deformation theory was described by Braverman and Joseph.
The same ideal appeared recently in connection with algebra of symmetries of differential operators. The paper presents a review of the corresponding circle of ideas and it discusses a role of special tensors in these questions.