Superpotentials and higher order derivations

Bocklandt, R., Schedler, T. and Wemyss, M. (2010) Superpotentials and higher order derivations. Journal of Pure and Applied Algebra, 214(9), pp. 1501-1522. (doi:10.1016/j.jpaa.2009.07.013)

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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) 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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Wemyss, Professor Michael
Authors: Bocklandt, R., Schedler, T., and Wemyss, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Pure and Applied Algebra
Publisher:Elsevier
ISSN:0022-4049
ISSN (Online):1873-1376
Published Online:01 February 2010
Copyright Holders:Copyright © 2010 Elsevier B.V.
First Published:First published in Journal of Pure and Applied Algebra 214(9):1501-1522
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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