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Title
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Superpotentials and higher order derivations
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Author
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Abstract
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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) CalabiYau 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 CalabiYau 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. |
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Language
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English
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Source (journal)
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Journal of pure and applied algebra. - Amsterdam
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Publication
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Amsterdam
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2010
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ISSN
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0022-4049
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DOI
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10.1016/J.JPAA.2009.07.013
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Volume/pages
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214
:9
(2010)
, p. 1501-1522
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ISI
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000275517700001
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Full text (Publisher's DOI)
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