Abstract
A minimal model for the associative algebra A is a quasi-free resolution (T(W),d) such that the differential map d maps W into ⊕ n≥2 W ⊗n . We would like to find a method to construct this minimal model when A is quadratic, that is A=T(V)/(R) where the ideal (R) is generated by R⊂V ⊗2. We will see that the quadratic data (V,R) permits us to construct explicitly a coalgebra Open image in new window and a twisting morphism Open image in new window . Then, applying the theory of Koszul morphisms given in the previous chapter, we obtain a simple condition which ensures that the cobar construction on the Koszul dual coalgebra, that is Open image in new window , is the minimal model of A.
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