Pointed Hopf algebras with standard braiding are generated in degree 1

ANGIONO, IVÁN; GARCÍA IGLESIAS, AGUSTÍN

CONTEMPORARY MATHEMATICS

AMS

Lugar: Providence; Año: 2011 vol. 537 p. 57 - 70

0271-4132

We show that any finite-dimensional pointed Hopf algebra over an abelian group $Gamma$ such that its infinitesimal braiding is of standard type is generated by group-like and skew-primitive elements. This fact agrees with the long-standing conjecture by Andruskiewitsch and Schneider. We also show that the quantum Serre relations hold in any coradically graded pointed Hopf algebra over $Gamma$ of finite dimension and determine how these relations are lifted in the standard case.