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ON POINTED HOPF ALGEBRAS ASSOCIATED WITH THE MATHIEU SIMPLE GROUPS

机译:与MATHIEU简单群相关的点Hopf代数

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摘要

Let G be a Mathieu simple group, s is an element of 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 = M-22 or M-24, then the group algebra of G is the only (up to isomorphisms) finite-dimensional complex pointed Hopf algebra with group-likes isomorphic to G.
机译:令G为Mathieu简单组,s为G的元素,O-s为s的共轭类,rho为s的中心化子的不可约表示。我们证明,要么Nichols代数B(O-s,rho)是无穷大的,要么是Butter-Drinfeld模块M(O-s,rho)的编织是负的。我们还表明,如果G = M-22或M-24,则G的群代数是唯一的(直至同构)有限维复尖的Hopf代数,其群相似于G。

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