There are exactly n isomorphism classes of infinitesimal commutative unipotent k-group schemes of order p^n with one-dimensional Lie algebra over an algebraically closed field of char p>0, with explicit descriptions provided.
Nguyen, Linhong Wang, and Xingting Wang
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Infinitesimal commutative unipotent group schemes with one-dimensional Lie algebra
There are exactly n isomorphism classes of infinitesimal commutative unipotent k-group schemes of order p^n with one-dimensional Lie algebra over an algebraically closed field of char p>0, with explicit descriptions provided.