A finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2)

NICOLÁS ANDRUSKIEWITSCH; IVÁN ANGIONO; FIORELA ROSSI BERTONE

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN

BELGIAN MATHEMATICAL SOC TRIOMPHE

Año: 2017 vol. 24 p. 15 - 34

1370-1444

Let Bq be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix q∈kθ×θ. Let Lq be the Lusztig algebra associated to Bq. We present Lq as an extension (as braided Hopf algebras) of Bq by Zq where Zq is isomorphic to the universal enveloping algebra of a Lie algebra nq. We compute the Lie algebra nq when θ=2.