The Green Rings of Taft algebras

Abstract

We compute the Green ring of the Taft algebra $H_n(q)$, where $n$ is a positive integer greater than 1, and $q$ is an $n$-th root of unity. It turns out that the Green ring $r(H_n(q))$ of the Taft algebra $H_n(q)$ is a commutative ring generated by two elements subject to certain relations defined recursively. Concrete examples for $n=2,3,...,8$ are given.

To appear in Proc. AMS

References in corpus (1)

• Periodicity of Adams operations on the Green ring of a finite group

Cited by in corpus (2)

• The Green rings of minimal Hopf quivers
• Green Rings of Finite Dimensional Pointed Rank One Hopf algebras of Nilpotent Type