Hopf coactions on commutative algebras generated by a quadratically independent comodule

Authors

Pavel Etingof, Massachusetts Institute of Technology
Debashish Goswami, Indian Statistical Institute, Kolkata
Arnab Mandal, Indian Statistical Institute, Kolkata
Chelsea Walton, Temple University

Article Type

Research Article

Publication Title

Communications in Algebra

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.

First Page

3410

Last Page

3412

DOI

10.1080/00927872.2016.1236934

Publication Date

8-3-2017

Comments

Open Access, Green

Recommended Citation

Etingof, Pavel; Goswami, Debashish; Mandal, Arnab; and Walton, Chelsea, "Hopf coactions on commutative algebras generated by a quadratically independent comodule" (2017). Journal Articles. 2458.
https://digitalcommons.isical.ac.in/journal-articles/2458