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- W1921569387 abstract "Let $G$ be a finite abelian group and let $L$ be a, possibly restricted, $G$-graded Lie color algebra. Then the enveloping algebra $U(L)$ is also $G$-graded, and we consider the question of whether $U(L)$ being graded-prime implies that it is prime. The first section of this paper is devoted to the special case of Lie superalgebras over a field $K$ of characteristic $neq 2$. Specifically, we show that if $i=sqrt {-1}in K$ and if $U(L)$ has a unique minimal graded-prime ideal, then this ideal is necessarily prime. As will be apparent, the latter result follows quickly from the existence of an anti-automorphism of $U(L)$ whose square is the automorphism of the enveloping algebra associated with its ${mathbb {Z}}_{2}$-grading. The second section, which is independent of the first, studies more general Lie color algebras and shows that if $U(L)$ is graded-prime and if most homogeneous components $L_{g}$ of $L$ are infinite dimensional over $K$, then $U(L)$ is prime. Here we use $Delta$-methods to study the grading on the extended centroid $C$ of $U(L)$. In particular, if $G$ is generated by the infinite support of $L$, then we prove that $C=C_{1}$ is homogeneous." @default.
- W1921569387 created "2016-06-24" @default.
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- W1921569387 date "1998-01-01" @default.
- W1921569387 modified "2023-10-18" @default.
- W1921569387 title "Enveloping algebras of Lie color algebras: Primeness versus graded-primeness" @default.
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- W1921569387 doi "https://doi.org/10.1090/s0002-9939-98-04372-x" @default.
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