Local criteria for cocommutative Hopf algebras
classification
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localcocommutativehopfonlyalgebraalgebrasconnectedcoradical
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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.
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