Noncommutative linear algebra and primitive ideals
Abstract: Many classical results about matrices involving the determinant, characteristic and minimal polynomials admit natural noncommutative generalizations. For example, the Capelli identity expresses a relation between the characteristic polynomials of AB and AtBt for certain matrices of differential operators. This is what I mean by "noncommutative linear algebra". This formalism throws new light on the known subtle differences between primitive ideals in the universal enveloping algebras and the coadjoint orbits.