Hello!

There is a theorem of Borel saying that:

For a connected cocommutative Hopf algebra $A$ over the perfect field $k$ such that underlying graded vector space is finite-dimensional over $k$ we have that $$A=\otimes_i A_i$$ where each $A_i$ is a Hopf algebra with a single generator

The question is - does this result hold if we replace $k$ with $k[t]$ and consider a connected cocommutative Hopf algebra $A$ over $k[t]$ such that $A$ is free as $k[t]$-module

There is a theorem of Borel saying that:

For a connected cocommutative Hopf algebra $A$ over the perfect field $k$ such that underlying graded vector space is finite-dimensional over $k$ we have that $$A=\otimes_i A_i$$ where each $A_i$ is a Hopf algebra with a single generator

The question is - does this result hold if we replace $k$ with $k[t]$ and consider a connected cocommutative Hopf algebra $A$ over $k[t]$ such that $A$ is free as $k[t]$-module