Primeness of the enveloping algebra of Hamiltonian superalgebras

Mark C. Wilson, Bulletin of the Australian Mathematical Society 56 (1997), 483-488.

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Abstract: In 1990 Allen Bell presented a sufficient condition for the primeness of the universal enveloping algebra of a Lie superalgebra. Let $latex Q$ be a nonsingular bilinear form on a finite-dimensional vector space over a field of characteristic zero. In this paper we show that Bell’s criterion applies to the Hamiltonian Cartan type superalgebras determined by $latex Q$, and hence obtain some new prime noetherian rings.