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Polytopal realizations of finite type $$\mathbf{g}$$-vector fans. (English) Zbl 1382.05075
Summary: This paper shows the polytopality of any finite type $$\mathbf{g}$$-vector fan, acyclic or not. In fact, for any finite Dynkin type $$\Gamma$$, we construct a universal associahedron $$\mathsf{Asso}_{\operatorname{un}}(\Gamma)$$ with the property that any $$\mathbf{g}$$-vector fan of type {$$\Gamma$$} is the normal fan of a suitable projection of $$\mathsf{Asso}_{\operatorname{un}}(\Gamma)$$.

##### MSC:
 5e+15 Combinatorial aspects of groups and algebras (MSC2010)
##### Keywords:
cluster algebras; generalized associahedra
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