Etingof, Pavel ; Goswami, Debashish ; Mandal, Arnab ; Walton, Chelsea (2016) Hopf coactions on commutative algebras generated by a quadratically independent comodule Communications in Algebra, 45 (8). pp. 3410-3412. ISSN 0092-7872 (In Press)
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Official URL: http://www.tandfonline.com/doi/abs/10.1080/0092787...
Related URL: http://dx.doi.org/10.1080/00927872.2016.1236934
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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Taylor & Francis Group. |
| Keywords: | Commutative Algebra; Co-semisimple Hopf Algebra; Hopf Algebra Action; Quadratic Independence |
| ID Code: | 102174 |
| Deposited On: | 01 Feb 2018 04:36 |
| Last Modified: | 01 Feb 2018 04:36 |
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