Title
Superpotentials and higher order derivationsSuperpotentials and higher order derivations
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Research group
Fundamental Mathematics
Publication type
article
Publication
Amsterdam,
Subject
Mathematics
Source (journal)
Journal of pure and applied algebra. - Amsterdam
Volume/pages
214(2010):9, p. 1501-1522
ISSN
0022-4049
ISI
000275517700001
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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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