Pointed Hopf algebras over the sporadic simple groups

Abstract

We show that every finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group is a group algebra, except for the Fischer group Fi22, the Baby Monster and the Monster. For these three groups, we give a short list of irreducible Yetter-Drinfeld modules whose Nichols algebra is not known to be finite-dimensional.

16 pages, final version

References in corpus (7)

• Finite-dimensional pointed Hopf algebras with alternating groups are trivial
• On pointed Hopf algebras associated with alternating and dihedral groups
• Some remarks on Nichols algebras
• On Nichols algebras over PGL(2,q) and PSL(2,q)
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Cited by in corpus (22)

• Finite-dimensional pointed Hopf algebras with alternating groups are trivial
• A classification of Nichols algebras of semi-simple Yetter-Drinfeld modules over non-abelian groups
• On the classification of quandles of low order
• Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type I. Non-semisimple classes in PSL(n,q)
• The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
• The classification of Nichols algebras over groups with finite root system of rank two
• Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
• On finite-dimensional copointed Hopf algebras over dihedral groups
• Nichols algebras over groups with finite root system of rank two II
• Right coideal subalgebras of Nichols algebras and the Duflo order on the Weyl groupoid
• 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
• The logbook of Pointed Hopf algebras over the sporadic groups
• Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V. Mixed classes in Chevalley and Steinberg groups
• New Large-Rank Nichols Algebras Over Nonabelian Groups With Commutator Subgroup Z_2
• Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules (over groups) of prime dimension
• 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
• Factorization of Graded Traces on Nichols Algebras
• Divisibility Relations for the Dimensions and Hilbert series of Nichols Algebras of Non-Abelian Group Type
• On Twisted homogeneous racks of type D