On pointed Hopf algebras associated with the Mathieu simple groups

Abstract

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

arXiv comment41 pages. Abstract and Theorem 1 (Table 1) modified; Subsection 1.3 added; Sections 2-6 (in version 1) put together in a Section 2 (in new version); Section 3 added. References: [AS1] removed, [AF3], [AFGV], [AHS] added. Cite in Theorem 1.2 corrected; Lemmata 1.4 and 1.5 (of v1) put together in Lemma 1.4 (of nv); Lemma 1.5 (of nv) briefly modified