Hopf coactions on commutative algebras generated by a quadratically independent comodule

Pavel Etingof; Debashish Goswami; Arnab Mandal; Chelsea Walton

doi:10.1080/00927872.2016.1236934

Hopf coactions on commutative algebras generated by a quadratically independent comodule

Pavel Etingof, Debashish Goswami, Arnab Mandal, Chelsea Walton

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	3410-3412
Number of pages	3
Journal	Communications in Algebra
Volume	45
Issue number	8
DOIs	https://doi.org/10.1080/00927872.2016.1236934
State	Published - 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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AU - Etingof, Pavel

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AU - Mandal, Arnab

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KW - Hopf algebra action

KW - co-semisimple Hopf algebra

KW - quadratic independence

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