Ideals in tensor powers of the enveloping algebra U(sl2)

Let Li = Ll(sl(2))(xn) be the tensor power of n, copies of the enveloping algebra U(sl(2)) over an arbitrary field K of characteristic zero. In this paper we list the prime ideals of U by generators and classify them by height. II Z is the center of U and J is a prime ideal of Z, there are exactly 2(s) prime ideals I of U with I boolean AND Z = J, where 0 less than or equal to s = s(J) less than or equal to n is an integer. Indeed, with respect to inclusion, they form a lattice isomorphic to the lattice of subsets of a set. When J is a maximal ideal of Z, there are only finitely many two-sided ideals of U containing J. They are presented by generators and their lattice is described. In particular, for each such J there exists a unique maximal ideal of U containing J and a unique ideal of U minimal with respect to the property that it properly contains JU. Similar results are given in the case when Li is the tensor product of infinitely many copies of U(sl(2)).