Hopf coactions on commutative algebras generated by a quadratically independent comodule. Issue 8 (3rd August 2017) - Etingof, Pavel
ABSTRACT: 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.