Some invariant subalgebras are graded isolated singularities

Abstract

In this note, we prove that the invariant subalgebra of the skew polynomial algebra k 〈 x 0 , x 1 , ⋯ , x n − 1 〉 / ( { x i x j + x j x i | i ≠ j } ) under the action x i ↦ x i + 1 ( i ∈ Z / n Z ) is a graded isolated singularity, and thus a conjecture of Chan-Young-Zhang is true.