Hopf coactions on commutative algebras generated by a quadratically independent comodule
Communications in Algebra
Let A be a commutative unital algebra over an algebraically closed field k of characteristic ≠ 2, whose generators form a finite-dimensional subspace V, with no nontrivial homogeneous quadratic relations. Let Q be a Hopf algebra that coacts on A inner-faithfully, while leaving V invariant. We prove that Q must be commutative when either: (i) the coaction preserves a non-degenerate bilinear form on V; or (ii) Q is co-semisimple, finite-dimensional, and char(k) = 0.
Etingof, Pavel; Goswami, Debashish; Mandal, Arnab; and Walton, Chelsea, "Hopf coactions on commutative algebras generated by a quadratically independent comodule" (2017). Journal Articles. 2458.