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ArticleOriginal scientific text

Title

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

Authors ¹

Affiliations

Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Abstract

Let H be a cocommutative connected Hopf algebra, where K is a field of characteristic zero. Let

H^{+} = K e r

and

h^{+} = h - (h)

for

h \in H

. We prove that

d_{h} = \sum_{r = 1}^{\infty} (\frac{{(- 1)}^{r + 1}}{r}) \sum h_{1}^{+} ... h_{r}^{+}

is primitive, where

\sum h_{1} \otimes ... \otimes h_{r} = Δ_{r - 1} (h)

.

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