By minimal K-T resolution you mean a CDGA which as an algebra $\mathcal A$ is a polynomial algebra on a nonnegatively graded vector space and whose differential lands in $\mathcal A^+\cdot\mathcal A^+$ q-iso to your initial algebra $A$?
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Mariano Suárez-Alvarez♦Jul 23 '13 at 6:32