Green rings of Nichols Hopf algebras K_m for m ≥ 2

Determine the Green ring r(K_m) for Nichols Hopf algebras K_m for all integers m ≥ 2.

Background

The Green ring of a Hopf algebra encodes fusion rules among all indecomposable modules and is typically much more complicated than the Grothendieck ring in the non-semisimple setting. While Green rings have been determined for certain classes (e.g., Taft algebras and the Drinfeld double of the Sweedler algebra), the general case of the Nichols Hopf algebras K_m is unresolved.

This paper determines r(K_2) using a relation to r(DK_1), thereby addressing one case, but the authors explicitly note the broader problem remains unknown for K_m with m ≥ 2.