The killing form of a hopf algebra and its radical

Abstract EN

In this paper, we define the Killing form for any finite dimensional Hopf algebras over a field k of characteristic 0, and investigate its fundamental properties.

Then we discuss the radical of the Killing form of some Hopf algebras, and give a criterion for a group algebra admitting non-degenerate Killing form.

Finally, we prove that the Killing form of a Hopf algebra is invariant under twisting, providing a way to construct new Hopf algebras with non-degenerate Killing form by twisting some groups.