  We classify Nichols algebras of irreducible Yetter-Drinfeld modules over
nonabelian groups satisfying an inequality for the dimension of the homogeneous
subspace of degree two. All such Nichols algebras are finite-dimensional, and
all known finite-dimensional Nichols algebras of nonabelian group type appear
in the result of our classification. We find a new finite-dimensional Nichols
algebra over fields of characteristic two.

Quantum Algebra