On Nichols algebras over SL(2,Fq) and GL(2,Fq)

Abstract

We compute necessary conditions on Yetter-Drinfeld modules over the groups SL(2,Fq) and GL(2,Fq) to generate finite dimensional Nichols algebras. This is a first step towards a classification of pointed Hopf algebras with a group of group-likes isomorphic to one of these groups.

Major exposition revision, including referees remarks. To appear in J. Math. Phys. 13 pages

References in corpus (1)

• On pointed Hopf algebras associated to unmixed conjugacy classes in S_n

Cited by in corpus (7)

• Finite-dimensional pointed Hopf algebras with alternating groups are trivial
• Pointed Hopf algebras over the sporadic simple groups
• On pointed Hopf algebras over dihedral groups
• Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type I. Non-semisimple classes in PSL(n,q)
• On Nichols algebras over PGL(2,q) and PSL(2,q)
• Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VI. Suzuki and Ree groups
• Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V. Mixed classes in Chevalley and Steinberg groups