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- W2963810136 abstract "This is a survey on pointed Hopf algebras over algebraically closed fields of characteristic 0. We propose to classify pointed Hopf algebras A by first determining the graded Hopf algebra grA associated to the coradical filtration of A. The A0-coinvariants elements form a braided Hopf algebra R in the category of Yetter–Drinfeld modules over the coradical A0 = |Γ, Γ the group of group-like elements of A, and gr A ' R#A0. We call the braiding of the primitive elements of R the infinitesimal braiding of A. If this braiding is of Cartan type [AS2], then it is often possible to determine R, to show that R is generated as an algebra by its primitive elements and finally to compute all deformations or liftings, that is pointed Hopf algebras such that gr A ' R#|Γ. In the last chapter, as a concrete illustration of the method, we describe explicitly all finite-dimensional pointed Hopf algebras A with abelian group of group-likes G(A) and infinitesimal braiding of type An (up to some exceptional cases). In other words, we compute all the liftings of type An; this result is our main new contribution in this paper." @default.
- W2963810136 created "2019-07-30" @default.
- W2963810136 creator A5068676400 @default.
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- W2963810136 date "2002-01-01" @default.
- W2963810136 modified "2023-10-01" @default.
- W2963810136 title "Pointed Hopf Algebras" @default.
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