THE NICHOLS ALGEBRA OF A SEMISIMPLE YETTER-DRINFELD MODULE By NICOLÁS ANDRUSKIEWITSCH, ISTVÁN HECKENBERGER, and HANS-JÜRGEN SCHNEIDER
نویسندگان
چکیده
We study the Nichols algebra of a semisimple Yetter-Drinfeld module and introduce new invariants including the notions of real roots and the Weyl groupoid. The crucial ingredient is a “reflection” defined on arbitrary such Nichols algebras. Our construction generalizes the restriction of Lusztig’s automorphisms of quantized Kac-Moody algebras to the nilpotent part. As a direct application we complete the classifications of finite-dimensional pointed Hopf algebras over S3, and of finite-dimensional Nichols algebras over S4. This theory has led to surprising new results in the classification of finite-dimensional pointed Hopf algebras with a non-abelian group of group-like elements.
منابع مشابه
Right Coideal Subalgebras of Nichols Algebras and the Duflo Order on the Weyl Groupoid
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