On finite GK-dimensional Nichols algebras of diagonal type: rank 3 and Cartan type

GARCÍA IGLESIAS, AGUSTÍN

Montevideo

Congreso; VI Congreso Latinoamericano de Matemáticos (CLAM IV) (online); 2021

It was conjectured by Andruskiewitsch ,Angiono and Heckenberger that a Nichols algebra of diagonal type with finite Gelfand-Kirillov dimension has finite (generalized) root system; they did in fact prove this for braidings of affine type or when the rank is two. We shall review some tools developed with the intention of proving this conjecture positively, in a work of Angiono and the author, and exhibit the proof for the rank 3 case, as well as for braidings of Cartan type.