Turkish Journal of Mathematics
DOI
10.3906/mat-1507-11
Abstract
In this paper, we intend to study idempotents of the Green algebra (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
First Page
789
Last Page
805
Recommended Citation
WANG, ZHIHUA
(2016)
"Idempotents of the Green algebras of finite dimensionalpointed rank one Hopf algebras of nilpotent type,"
Turkish Journal of Mathematics: Vol. 40:
No.
4, Article 8.
https://doi.org/10.3906/mat-1507-11
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss4/8
