Idempotents of the Green algebras of finite dimensional pointed rank one Hopf algebras of nilpotent type

Authors : Zhihua WANG

Pages : 789-805

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we intend to study idempotents of the Green algebra insert ignore into journalissuearticles values(complexified Green ring); of any finite dimensional pointed rank one Hopf algebra of nilpotent type over the complex number field. We first determine all one dimensional representations of the quotient algebra of the Green algebra modulo its Jacobson radical. This gives rise to all primitive idempotents of the quotient algebra. Then we present explicitly primitive idempotents of the Green algebra by lifting the ones of the quotient algebra. Finally, as an example, we describe all primitive idempotents of the Green algebra of the Taft algebra $T_3$.
Keywords : Hopf algebra, Green algebra, idempotent, Dickson polynomial