The radical of the restricted universal enveloping algebra of A1

Document Type

Article

Publication Date

1-1-1983

Abstract

Let ? be the classical Lie algebra of type A1 with a basis {e, f, h} and [e, f] = h, [e, h] = 2e, [f, h] = -2f over an algebraically closed field of characteristic p > 2. Let ? be the radical of the u-algebra U of ?. Our main result is the obtainment of (p - 1)/2 sets of generators ?, and hence (p - 1)/2 criteria for complete reducibility of restricted representations of ?. © 1983 Rocky Mountain Mathematics Consortium.

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