A DOMAIN TEST FOR LIE COLOR ALGEBRAS

Abstract

Lie color algebras are generalizations of Lie superalgebras and graded Lie algebras. The properties of a Lie color algebra can often be related directly to the ring structure of its universal enveloping algebra. We study the effects of torsion elements and torsion subspaces. Let [Formula: see text] denote a Lie color algebra. If [Formula: see text] is homogeneous and torsion then x2 = 0 in [Formula: see text]. If no homogeneous element of [Formula: see text] is torsion, then [Formula: see text] so [Formula: see text] is semiprime. In this case we can give a test which uses Gröbner basis methods to determine when [Formula: see text] is a domain. This is applied in an example to show [Formula: see text] may be a domain even if [Formula: see text] contains torsion elements and torsion subspaces.