On pointed Hopf algebras associated with the Mathieu simple groups

Let G be a Mathieu simple group, s in G, O_s the conjugacy class of s and \rho an irreducible representation of the centralizer of s. We prove that either the Nichols algebra B(O_s,\rho) is infinite-dimensional or the braiding of the Yetter-Drinfeld module M(O_s, \rho) 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.