Finite GK-dimensional pre-Nichols algebras of quantum linear spaces and of Cartan type

Andruskiewitsch, Nicolás; Sanmarco, Guillermo

doi:10.1090/btran/66

Finite GK-dimensional pre-Nichols algebras of quantum linear spaces and of Cartan type
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Trans. Amer. Math. Soc. Ser. B 8 (2021), 296-329

Abstract:

We study pre-Nichols algebras of quantum linear spaces and of Cartan type with finite GK-dimension. We prove that except for a short list of exceptions involving only roots of order 2, 3, 4, 6, any such pre-Nichols algebra is a quotient of the distinguished pre-Nichols algebra introduced by Angiono generalizing the De Concini-Kac-Procesi quantum groups. There are two new examples, one of which can be thought of as $G_2$ at a third root of one.

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