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What are the big problems which will guide future research into locally nilpotent derivations? Certainly, any answer I give reflects my own point of view, and we have good reason to “expect the unexpected”. There is tremendous room for further research into the locally nilpotent derivations of other commutative rings, like power series rings, or integral domains not containing a field, or of non-commutative rings, including Lie algebras, quantum polynomial rings, universal enveloping algebras, and the like. Some of these investigations have been started by Makar-Limanov (see [190, 197]).
KeywordsPolynomial Ring Reductive Group Extension Property Power Series Ring Invariant Ring
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