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On some formula in connected cocommutative Hopf algebras over a field of characteristic 0

100%

Wiśniewski P.

Colloquium Mathematicum

2000

tom 83

nr 2

271-279

Let H be a cocommutative connected Hopf algebra, where K is a field of characteristic zero. Let $H^{+} = Ker 𝜺$ and $h^{+} = h - 𝜺(h)$ for $h ∈ H$. We prove that $d_h = ∑_{r=1}^∞ ((-1)^{r+1}/r) ∑ h_1^{+}...h_r^{+}$ is primitive, where $∑ h_1 ⊗ ... ⊗ h_r=Δ_{r-1}(h)$.