Delta ideals of Lie color algebras (Q1904238)

Let \(L\) be a Lie color algebra, possibly restricted, over a field \(K\) and graded by a finite abelian group \(G\). The authors show that if \(L\) has no nonzero elements with centralizers of countable codimension, then its enveloping algebra \(U(L)\) is ``symmetrically closed'' in the sense that it coincides with its symmetric Martindale quotient ring [see the second author, J. Algebra 105, 207-235 (1987; Zbl 0605.16003) for the definition]. They also show that the Lie color ideal \(\Delta(L)\) consisting of the elements whose centralizers have finite codimension has derived subalgebra sitting inside the join \(\Delta_L\) of all the finite-dimensional Lie color ideals of \(L\). These results are new even for ordinary or super Lie algebras.