The Super-Rank of a Locally Nilpotent Derivation of a Polynomial Ring

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 319)


The super-rank of a k-derivation of a polynomial ring \(k^{[n]}\) over a field k of characteristic zero is introduced. Like rank, super-rank is invariant under conjugation, and thus gives a way to classify derivations of maximal rank n. For each \(m\ge 2\), we construct a locally nilpotent derivation of \(k^{[m(m+1)]}\) with maximal super-rank \(m(m+1)\).


Locally nilpotent derivation Additive group action Determinantal variety 

2010 Mathematics Subject Classification

13A50 13N15 14M12 14R20 



The author wishes to thank Steve Mackey of Western Michigan University for his comments about an earlier version of this paper which led to a number of improvements in the final version.


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Authors and Affiliations

  1. 1.Department of MathematicsWestern Michigan UniversityKalamazooUSA

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