Hopf coactions on commutative algebras generated by a quadratically independent comodule

Pavel Etingof, Debashish Goswami, Arnab Mandal, Chelsea Walton

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)3410-3412
Number of pages3
JournalCommunications in Algebra
Volume45
Issue number8
DOIs
StatePublished - Aug 3 2017

Keywords

  • Commutative algebra
  • Hopf algebra action
  • co-semisimple Hopf algebra
  • quadratic independence

ASJC Scopus subject areas

  • Algebra and Number Theory

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