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

• Autorzy: Piotr Wiśniewski
• Języki publikacji: EN

Abstrakty

EN

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 $∑ h_1 ⊗ ... ⊗ h_r=Δ_{r-1}(h)$.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 83
• Numer: 2
• Strony: 271-279

Daty

wydano

2000

otrzymano

1999-10-12

poprawiono

1999-11-03

Twórcy

autor

Piotr Wiśniewski

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

Bibliografia

• [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.
• [3] M. E. Sweedler, Hopf Algebras, Benjamin, New York, 1969.
• [4] N. Ya. Vilenkin, Combinatorics, Academic Press, New York, 1971.