On a conjecture of Kontsevich and Soibelman

Abstract

We consider a conjecture of Kontsevich and Soibelman which is regarded as a foundation of their theory of motivic Donaldson-Thomas invariants for non-commutative 3d Calabi-Yau varieties. We will show that, in some certain cases, the answer to this conjecture is positive.Comment: 14 pages, to appear in Algebra and Number Theory (2012