On pointed Hopf algebras associated with the Mathieu simple groups
Abstract
Let G be a Mathieu simple group, s in G, Os the conjugacy class of s and an irreducible representation of the centralizer of s. We prove that either the Nichols algebra B(Os,) is infinite-dimensional or the braiding of the Yetter-Drinfeld module M(Os, ) is negative. We also show that if G=M22 or M24, then the group algebra of G is the only (up to isomorphisms) finite-dimensional complex pointed Hopf algebra with group-likes isomorphic to G.
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