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.
Original language | English (US) |
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Pages (from-to) | 3410-3412 |
Number of pages | 3 |
Journal | Communications in Algebra |
Volume | 45 |
Issue number | 8 |
DOIs | |
State | Published - Aug 3 2017 |
Keywords
- Commutative algebra
- Hopf algebra action
- co-semisimple Hopf algebra
- quadratic independence
ASJC Scopus subject areas
- Algebra and Number Theory