Geoffrey Pritchard and Mark C. Wilson, Archiv der Mathematik 70 (1998), 187-196.
Abstract: A primeness criterion due to Bell is shown to apply to the universal enveloping algebra of the Cartan type Lie superalgebras $latex S(V)$ and $latex widetilde{S}(V;t)$ when $latex dim V$ is even.
Mark C. Wilson, Journal of Pure and Applied Algebra 133 (1998), 241-260.
Abstract: We determine all finite-dimensional simple Lie superalgebras $latex L$ such that $latex U(L)$ satisfies a primeness criterion due to Bell. Some open problems related to primeness of enveloping algebras are listed.
Geoffrey Pritchard and Mark C. Wilson, Experimental Mathematics 6 (1997), 77-85.
Abstract: On the basis of experimental work involving matrix computations, we conjecture that a criterion due to Bell for primeness of the universal enveloping algebra of a Lie superalgebra applies to the Cartan type Lie superalgebras $latex W(n)$ for $latex n=3$ but does not apply for odd $latex ngeq 5$. The experiments lead to a rigorous proof, which we present.
Mark C. Wilson, Bulletin of the Australian Mathematical Society 56 (1997), 483-488.
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.
Mark C. Wilson, Communications in Algebra 25 (1997), 487-496.
Abstract:
Let $latex K$ be a field of characteristic $latex p>0$, let $latex L$ be a restricted Lie algebra and let $latex R$ be an associative $latex K$-algebra. It is shown that the various constructions in the literature of crossed product of $latex R$ with $latex u(L)$ are equivalent. We calculate explicit formulae relating the parameters involved and obtain a formula which hints at a noncommutative version of the Bell polynomials.
Mark C. Wilson, Proceedings of the American Mathematical Society 124 (1996), 383-387.
Abstract: We show that a primeness criterion for enveloping algebras of Lie superalgebras discovered by Bell is applicable to the Cartan type Lie superalgebras $latex W(n)$, $latex n$ even. Other algebras are considered but there are no definitive answers in these cases.
Mark C. Wilson, Journal of Algebra 175 (1995), 661-696.
Abstract: 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 $latex L$ is a Lie colour algebra then the join of all finite-dimensional ideals of $latex L$ controls certain properties of the universal enveloping algebras $latex U(L)$. Specifically, we consider primeness, semiprimeness, constants, semi-invariants, almost constants, faithfulness of the adjoint action, the centre, almost centralizers and the central closure.