On Nichols algebras with standard braiding

The class of standard braided vector spaces, introduced by Andruskiewitsch and the author in $\mathtt{\text{arXiv:math/0703924v2}}$ to understand the proof of a theorem of Heckenberger \cite{H2}, is slightly more general than the class of braided vector spaces of Cartan type. In the present paper, we classify standard braided vector spaces with finite-dimensional Nichols algebra. For any such braided vector space, we give a PBW-basis, a closed formula of the dimension and a presentation by generators and relations of the associated Nichols algebra.