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Serre duality is a duality present on non-singular projective algebraic varieties V of dimension n (and in greater generality for vector bundles and further, for coherent sheaves)

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Serre functor of the graded dual number

Consider the dg-algebra $A=\mathbb{C}[x]/x^2$, where $deg(x)=-k$ for some $k\geq0$. Is it known what is the Serre functor of $D^{\mathrm{perf}}(A)$?
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