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Rigidity of down-up algebras with respect to finite group coactions (1606.08428v1)
Published 27 Jun 2016 in math.RA
Abstract: If a nontrivial finite group coacts on a graded noetherian down-up algebra $A$ inner faithfully and homogeneously, then the fixed subring is not isomorphic to $A$. Therefore graded noetherian down-up algebras are rigid with respect to finite group coactions, in the sense of Alev-Polo. An example is given to show that this rigidity under group coactions does not have all the same consequences as the rigidity under group actions.
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