Finite GK-dimensional pre-Nichols algebras of (super)modular and unidentified type

ANGIONO, IVÁN; CAMPAGNOLO, EMILIANO; SANMARCO, GUILLERMO

JOURNAL OF NONCOMMUTATIVE GEOMETRY

EUROPEAN MATHEMATICAL SOC

Año: 2023

1661-6952

We show that every finite GK-dimensional pre-Nichols algebra for braidings of diagonal type with connected diagram of modular, supermodular or unidentified type is a quotient of the distinguished pre-Nichols algebra introduced by the first-named author, up to two exceptions. For both of these exceptional cases, we provide a pre-Nichols algebra that substitutes the distinguished one in the sense that it projects onto all finite GK-dimensional pre-Nichols algebras. We build these two substitutes as non-trivial central extensions with finite GK-dimension of the corresponding distinguished pre-Nichols algebra. We describe these algebras by generators and relations, and provide a basis. This work essentially completes the study of eminent pre-Nichols algebras of diagonal type with connected diagram and finite-dimensional Nichols algebra.