Delta Methods in Enveloping Algebras of Lie Color Algebras Original Research Article

In recent papers J. Bergen and D. S. Passman have applied so-called "Delta methods" to enveloping algebras of Lie superalgebras. This paper generalizes their results to the class of Lie colour algebras. The methods and results in this paper are very similar to those of Bergen and Passman, and many of their proofs generalize easily. However, at some points there are serious difficulties to overcome. The results obtained show that if L is a Lie colour algebra then the join of all finite-dimensional ideals of L, denoted ΔL, controls certain properties of the universal enveloping algebra U(L). Specifically, we consider primeness, semiprimeness, constants, semi-invariants, almost constants, faithfulness of the adjoint action, the centre, almost centralizers, and the central closure.