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- Title
Finite GK-dimensional pre-Nichols algebras of (super)modular and unidentified type.
- Authors
Angiono, Iván; Campagnolo, Emiliano; Sanmarco, Guillermo
- 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.
- Subjects
LIE superalgebras; ALGEBRA; RELATION algebras; HOPF algebras
- Publication
Journal of Noncommutative Geometry, 2023, Vol 17, Issue 2, p499
- ISSN
1661-6952
- Publication type
Article
- DOI
10.4171/JNCG/497