Local criteria for cocommutative Hopf algebras

Abstract

We prove that a finite-dimensional cocommutative Hopf algebra $H$ is local, if and only if the subalgebra generated by the first term of its coradical filtration $H_1$ is local. In particular if $H$ is connected, $H$ is local if and only if all the primitive elements of $H$ are nilpotent.

11 pages, no figures

References in corpus (2)

• Connected Hopf Algebras of Dimension $p^2$
• Classification of pointed Hopf algebras of dimension $p^2$ over any algebraically closed field

Cited by in corpus (2)

• Classification of connected Hopf algebras of dimension $p^3$ I
• Isomorphism classes of finite dimensional connected Hopf algebras in positive characteristic