Commutative Hopf structures over a loop

Details Commutative Hopf structures over a loop Commutative Hopf structures over a loop

2010-02-02

arxiv.org/abs/1002.0405v1

Mathematics

Rings and Algebras

16 pages

Scientific paper

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.

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