Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type I. Non-semisimple classes in PSL(n,q)

Abstract

We show that Nichols algebras of most simple Yetter-Drinfeld modules over the projective special linear group over a finite field, corresponding to non-semisimple orbits, have infinite dimension. We spell out a new criterium to show that a rack collapses.

minor changes, to appear in Journal of Algebra

Cited by in corpus (11)

• On Hopf Algebras over quantum subgroups
• On finite-dimensional copointed Hopf algebras over dihedral groups
• Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type III. Semisimple classes in PSL(n,q)
• Finite-dimensional Hopf algebras over the Hopf algebra $H_{b:1}$ of Kashina
• 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
• On some classification of finite-dimensional Hopf algebras over the Hopf algebra $H_{b:1}^{\ast }$ of Kashina
• Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules (over groups) of prime dimension
• Pointed Hopf Algebras with Triangular Decomposition -- A Characterization of Multiparameter Quantum Groups
• Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VII. Semisimple classes in PSL(n,q) and PSp(2n,q)
• Twisted homogeneous racks over the alternating groups