Details:
Title  Superpotentials and higher order derivations  Author(s)  Raf Bocklandt, Travis Schedler, Michael Wemyss  Type  Article in Journal  Abstract  We consider algebras defined from quivers with relations that are k th order derivations of a superpotential, generalizing results of DuboisViolette 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 GL n for all n , and fourdimensional 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 fourdimensional Sklyanin algebras using the Weil representation of an extension of SL 2 ( Z / 4 ) .  ISSN  00224049 
URL 
http://www.sciencedirect.com/science/article/pii/S002240490900173X 
Language  English  Journal  Journal of Pure and Applied Algebra  Volume  214  Number  9  Pages  1501  1522  Year  2010  Edition  0  Translation 
No  Refereed 
No 
