Abstract
The powerful concept of Gröbner bases and an extension of the Buchberger algorithm for their computation have been generalised to enveloping algebras of Lie algebras. Algorithms for the computation of syzygies by use of Gröbner bases are given. This is the first method which allows the transformation of right fractions into left fractions in the Lie field of any finite dimensional Lie algebra. That enables CAS calculations in Lie fields. An AMP program LIEFIELD has been written for this purpose. Another AMP program SYZYGY produces a generating set of the syzygy module of any finite subset of an enveloping algebra. Examples for both programs are presented for the Weyl algebra and the so(3).
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