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arXiv · 1507.08486

Hopf coactions on commutative algebras generated by a quadratically independent comodule

Pavel Etingof·Debashish Goswami·Arnab Mandal·Chelsea Walton
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Abstract

Let A be a commutative unital algebra over an algebraically closed field k of characteristic not equal to 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.

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Pavel Etingof, Debashish Goswami, Arnab Mandal, Chelsea Walton. 2016-03-03. Hopf coactions on commutative algebras generated by a quadratically independent comodule. https://arxiv.org/abs/1507.08486

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