Representations of copointed Hopf algebras arising from the tetrahedron rack

Abstract

We study the copointed Hopf algebras attached to the Nichols algebra of the affine rack \(\Aff(\F_4,\omega)\), also known as tetrahedron rack, and the 2-cocycle -1. We investigate the so-called Verma modules and classify all the simple modules. We conclude that these algebras are of wild representation type and not quasitriangular, also we analyze when these are spherical.