%0 Journal Article
%T Commutative Hopf structures over a loop
%A Hua-Lin Huang
%A Gongxiang Liu
%A Yu Ye
%J Mathematics
%D 2010
%I arXiv
%X Let $k$ be an algebraically closed field of characteristic $p>0$. For a loop $\circlearrowleft$, denote its path coalgebra by $k\circlearrowleft$. In this paper, all the finite-dimensional commutative Hopf algebras over the sub coalgebras of $k\circlearrowleft$ are given. As a direct consequence, all the commutative infinitesimal groups $\mathcal{G}$ with dim$_{k}$Lie$(\mathcal{G})=1$ are classified.
%U http://arxiv.org/abs/1002.0405v1