Title of article :
THE KILLING FORM OF A HOPF ALGEBRA AND ITS RADICAL
Author/Authors :
Wang, Zhihua Nanjing Normal University - Taizhou College - Department of Mathematics, China , Chen, Huixiang Yangzhou University - School of Mathematics, China , Li, Libin Yangzhou University - School of Mathematics, China
Abstract :
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.
Keywords :
Hopf algebra , Killing form , radical , adjoint representation
Journal title :
The Arabian Journal for Science and Engineering
Journal title :
The Arabian Journal for Science and Engineering
