Pointed Hopf algebras with standard braiding are generated in degree one

Details Pointed Hopf algebras with standard braiding are generated in degree one Pointed Hopf algebras with standard braiding are generated in degree one

2010-04-19

arxiv.org/abs/1004.3312v1

Mathematics

Quantum Algebra

15 pages

Scientific paper

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.

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