Nichols Algebras and Quantum Principal Bundles

Abstract

A general procedure for constructing Yetter-Drinfeld modules from quantum principal bundles is introduced. As an application a Yetter-Drinfeld structure is put on the cotangent space of the Heckenberger-Kolb calculi of the quantum Grassmannians. For the special case of quantum projective space the associated braiding is shown to be non-diagonal and of Hecke type. Moreover, its Nichols algebra is shown to be finite-dimensional and equal to the anti-holomorphic part of the total differential calculus.Comment: Updated grant details. arXiv admin note: text overlap with arXiv:1611.0796