Andruskiewitsch–Schneider generation-in-degree-one conjecture

Prove that for any finite group G and any finite-dimensional coradically graded connected Hopf algebra R in the Yetter–Drinfeld category over kG, the algebra R is generated by its degree-one component R^1; equivalently, establish that R equals the Nichols algebra B(R^1).

Background

The Lifting Method reduces the classification of finite-dimensional pointed Hopf algebras to three steps, the second of which asks for the structure of coradically graded connected Hopf algebras R given an infinitesimal braiding V. The conjecture asserts that any such finite-dimensional R must coincide with the Nichols algebra B(V), i.e., be generated in degree one. This result is known in several cases (e.g., abelian coradical and various non-abelian settings) but remains open in general.