Locally Nilpotent Derivations, A New Ring Invariant and Applications

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MAKAR-LIMANOV, ABSTRACT 9700894 The main objects of the research in this proposal are locally nilpotent derivations on various algebra, a new invariant which was recently introduced by the principal investigator, and their possible applications to algebraic and geometric questions. The motivation of this research is the development of algebraic tools which allow one to distinguish rings (in commutative and non-commutative settings). The invariant which was originally introduced in order to distinguish some factor-rings of a polynomial ring with four generators also is useful in a description of groups of automorphisms of a certain class of surfaces and in cancellation type problems. Ring theory and group theory provide a means for describing geometric objects through the study of certain properties like symmetry and reflections and how these "operations" leave "invariant" certain geometric features of the objects of study.