Hopf coactions on commutative algebras generated by a quadratically independent comodule
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1507.08486.pdf
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Author(s)
Goswami, Debashish
Mandal, Arnab
Walton, Chelsea
Etingof, Pavel I
Date Issued
October 2016
Journal
Communications in Algebra
Publisher
Taylor & Francis
Citation
Etingof, Pavel et al. “Hopf Coactions on Commutative Algebras Generated by a Quadratically Independent Comodule.” Communications in Algebra 45, 8 (October 2016): 3410–3412 © 2016 Taylor & Francis
Version
Original manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1080/00927872.2016.1236934
