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Lookup NU author(s): Dr Rafael Bocklandt
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We consider algebras defined from quivers with relations that are kth order derivations of a superpotential, generalizing results of Dubois-Violette to the quiver case. We give a construction compatible with Morita equivalence, and show that many important algebras arise in this way, including McKay correspondence algebras for View the MathML source for all n, and four-dimensional Sklyanin algebras. More generally, we show that any N-Koszul, (twisted) Calabi–Yau algebra must have a (twisted) superpotential, and construct its minimal resolution in terms of derivations of the (twisted) superpotential. This yields an equivalence between N-Koszul twisted Calabi–Yau algebras A and algebras defined by a superpotential ω such that an associated complex is a bimodule resolution of A. Finally, we apply these results to give a description of the moduli space of four-dimensional Sklyanin algebras using the Weil representation of an extension of View the MathML source.
Author(s): Bocklandt R, Schedler T, Wemyss M
Publication type: Article
Publication status: Published
Journal: Journal of Pure and Applied Algebra
Year: 2010
Volume: 214
Issue: 9
Pages: 1501-1522
Print publication date: 01/02/2010
ISSN (print): 0022-4049
ISSN (electronic): 1873-1376
Publisher: Elsevier BV
URL: http://dx.doi.org/10.1016/j.jpaa.2009.07.013
DOI: 10.1016/j.jpaa.2009.07.013
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