Finite GK-dimensional pre-Nichols algebras of (super)modular and unidentified type
Iván Ezequiel Angiono
Universidad Naciona de Córdoba, ArgentinaEmiliano Campagnolo
Universidad Naciona de Córdoba, ArgentinaGuillermo Sanmarco
Iowa State University, Ames, USA
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Abstract
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 these two 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 both 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 give a basis. This work essentially completes the study of eminent pre-Nichols algebras of diagonal type with connected diagram and finite-dimensional Nichols algebra.
Cite this article
Iván Ezequiel Angiono, Emiliano Campagnolo, Guillermo Sanmarco, Finite GK-dimensional pre-Nichols algebras of (super)modular and unidentified type. J. Noncommut. Geom. 17 (2023), no. 2, pp. 499–525
DOI 10.4171/JNCG/497