Rigidity of maps from Hopf algebras to group algebras
It is well-known in the theory of algebraic groups that one cannot deform maps from a diagonalizable group to a linear algebraic group except trivially, i.e., by conjugation with inner automorphisms of the target. This note gives a noncommutative analogue of this result in which linear algebraic groups are replaced by finitely generated bialgebras and diagonal groups are replaced by cancellative monoid algebras. The underlying field must be algebraically closed of characteristic zero. The arguments are Hopf-algebra theoretic with some differential algebra.
scientific article; zbMATH DE number 4059604