Lie Algebras Arising from Nichols Algebras of Diagonal Type

ANDRUSKIEWITSCH, NICOLÁS; ANGIONO, IVÁN; FIORELA ROSSI BERTONE

INTERNATIONAL MATHEMATICS RESEARCH NOTICES

OXFORD UNIV PRESS

Año: 2022

1073-7928

Let $mathcal{B}_{mathfrak{q}}$ be a finite-dimensional Nichols algebra of diagonal type with braiding matrix $mathfrak{q}$, let $mathcal{L}_{mathfrak{q}}$ be the corresponding Lusztig algebra as in cite{AAR1} and let $operatorname{Fr}_{mathfrak{q}}: mathcal{L}_{mathfrak{q}} o U(mathfrak{n}^{mathfrak{q}})$ be the corresponding quantum Frobenius map as in cite{AAR2}. We prove that the finite-dimensional Lie algebra $mathfrak{n}^{mathfrak{q}}$ is either 0 or else the positive part of a semisimple Lie algebra $mathfrak{g}^mathfrak{q}$which is determined for each $mathfrak{q}$ in the list of cite{H-classif RS}.