Lie algebras arising from Nichols algebras of diagonal type

NICOLÁS ANDRUSKIEWITSCH; ANGIONO, IVÁN EZEQUIEL; FIORELA ROSSI BERTONE

INTERNATIONAL MATHEMATICS RESEARCH NOTICES

OXFORD UNIV PRESS

Lugar: Oxford; Año: 2021

1073-7928

Let B𝔮 be a finite-dimensional Nichols algebra of diagonal type with braiding matrix 𝔮, L𝔮 be the corresponding Lusztig algebra as in [ 4], and Fr𝔮:L𝔮→U(𝔫𝔮) be the corresponding quantum Frobenius map as in [5]. We prove that the finite-dimensional Lie algebra 𝔫𝔮 is either 0 or the positive part of a semisimple Lie algebra 𝔤𝔮⁠, which is determined for each 𝔮 in the list of [ 25].