Calabi-Yau algebras and superpotentials

By Michel van den Bergh. 2010

157 citations recorded by the source corpus.

We prove that complete $$d$$d-Calabi-Yau algebras in the sense of Ginzburg are derived from superpotentials.

Subfields: Algebra and Number Theory, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/60127e3143d3718ad4627888e40bc196e7b52eae

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Citations in the corpus

Noncommutative deformations and flops (2013, background): “n, which is the same as Reid’s width. (⇒) By contrapositive. Suppose that C is a (−3,1)-curve. Since U is smooth, A is a NCCR, and since Ris complete local, A is given by an admissible superpotential [V10]. Since Cis a (−3,1)-curve, there are two loops at the vertex corresponding to S, since the num”
Skew Calabi–Yau algebras and homological identities (2013, methodology): “gories, string theory and conformal ﬁeld theory, noncommutative crepant resolutions, and Donaldson-Thomas invariants. Some fundamental questions in the area were answered by Van den Bergh recently in [VdB3]. One known method for constructing a noncommutative Calabi-Yau algebra is to form the smash p”
Representations of Algebras and Related Topics (2011, background): “tion 2.20 (2) in the Jacobi-ﬁnite case. Remark 3.12. If (Q,W) is not Jacobi-ﬁnite, a generalization of the category C(Q,W), which is not Hom-ﬁnite, is constructed in [81]. Note that in a recent paper [91], Van den Bergh has shown that complete DG algebras in negative degrees which are bimodule 3-Cal”
Almost complete cluster tilting objects in generalized higher cluster categories (2010, methodology): “uperpotential being a linear combination of paths of QV of degree 1−m and of length ≥ 3, hold, then we will say that the completed deformed preprojective dg algebra Π(b Q,m+2,W) is good. Theorem 4.7 ([30]). Let A be a strongly (m + 2)-Calabi-Yau dg algebra with components concentrated in degrees ≤ 0”