On the Hopf Algebra Structure of the Lusztig Quantum Divided Power Algebras

NICOLÁS ANDRUSKIEWITSCH; IVÁN ANGIONO; CRISTIAN VAY

Annales Mathématiques Blaise Pascal

Centre Mersenne

Año: 2020 vol. 271 p. 131 - 157

We study the Hopf algebra structure of Lusztig´s quantum groups. First weshow that the zero part is the tensor product of the group algebra of a finiteabelian group with the enveloping algebra of an abelian Lie algebra. Second webuild them from the plus, minus and zero parts by means of suitable actions andcoactions within the formalism presented by Sommerhauser to describe triangulardecompositions.