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We study the Nichols algebra of a semisimple Yetter-Drinfeld module and introduce new invariants such as real roots. The crucial ingredient is a “reflection” in the class of such Nichols algebras. We conclude the classifications of finite-dimensional pointed Hopf algebras over S3, and of finite-dimensional Nichols algebras over S4.
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Andruskiewitsch et al. (2010) studied this question.
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