On pointed Hopf algebras associated with the Mathieu simple groups

Details On pointed Hopf algebras associated with the Mathieu simple groups On pointed Hopf algebras associated with the Mathieu simple groups

2007-11-20

arxiv.org/abs/0711.3142v2

J. Algebra Appl., Vol 8, No. 5 (2009), Pages 633-672

Mathematics

Quantum Algebra

41 pages. Abstract and Theorem 1 (Table 1) modified; Subsection 1.3 added; Sections 2-6 (in version 1) put together in a Secti

Scientific paper

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.

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