Hopf coactions on commutative algebras generated by a quadratically independent comodule
Author(s)Goswami, Debashish; Mandal, Arnab; Walton, Chelsea; Etingof, Pavel I
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Communications in Algebra
Taylor & Francis
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