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

Colloquium Mathematicae (2000)

- Volume: 83, Issue: 2, page 271-279
- ISSN: 0010-1354

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topWiśniewski, Piotr. "On some formula in connected cocommutative Hopf algebras over a field of characteristic 0." Colloquium Mathematicae 83.2 (2000): 271-279. <http://eudml.org/doc/210786>.

@article{Wiśniewski2000,

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

author = {Wiśniewski, Piotr},

journal = {Colloquium Mathematicae},

keywords = {Hopf algebras; derivations; primitive elements; enveloping algebras; counits},

language = {eng},

number = {2},

pages = {271-279},

title = {On some formula in connected cocommutative Hopf algebras over a field of characteristic 0},

url = {http://eudml.org/doc/210786},

volume = {83},

year = {2000},

}

TY - JOUR

AU - Wiśniewski, Piotr

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

JO - Colloquium Mathematicae

PY - 2000

VL - 83

IS - 2

SP - 271

EP - 279

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

LA - eng

KW - Hopf algebras; derivations; primitive elements; enveloping algebras; counits

UR - http://eudml.org/doc/210786

ER -

## References

top- [1] S. Montgomery, Hopf Algebras and Their Actions on Rings, CBMS Regional Conf. Ser. in Math. 82, Amer. Math. Soc., Providence, RI, 1993.
- [2] S. A. Saymeh, On Hasse-Schmidt higher derivations, Osaka J. Math. 23 (1986), 503-508. Zbl0609.13017
- [3] M. E. Sweedler, Hopf Algebras, Benjamin, New York, 1969.
- [4] N. Ya. Vilenkin, Combinatorics, Academic Press, New York, 1971.

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