Hopf coactions on commutative algebras generated by a quadratically independent comodule. Issue 8 (3rd August 2017)

• Record Type: Journal Article
• Authors: Etingof, Pavel; Goswami, Debashish; Mandal, Arnab; Walton, Chelsea
• Is Part Of: Communications in algebra. Volume 45:Issue 8(2017)
• Page Start: 3410
• Page End: 3412
• Publication Date: 2017-08-03
• Subjects: Commutative algebra -- co-semisimple Hopf algebra -- Hopf algebra action -- quadratic independence; 16T05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1236934
• Languages: English
• ISSNs: 0092-7872

Abstract

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.