@article{f591cad51b69440e8c5cb72680ed5204,
title = "Representation theory of three-dimensional Sklyanin algebras",
abstract = "We determine the dimensions of the irreducible representations of the Sklyanin algebras with global dimension 3. This contributes to the study of marginal deformations of the N= 4 super Yang-Mills theory in four dimensions in supersymmetric string theory. Namely, the classification of such representations is equivalent to determining the vacua of the aforementioned deformed theories. We also provide the polynomial identity degree for the Sklyanin algebras that are module finite over their center. The Calabi-Yau geometry of these algebras is also discussed.",
author = "Chelsea Walton",
note = "Funding Information: Most of the results in this article were part of my Ph.D. thesis at the University of Michigan, and I thank my adviser Toby Stafford for his guidance on this project. Moreover, I thank David Berenstein, Kenneth Chan, David Morrison, Michael Wemyss, and Leo Pando Zayas for supplying many insightful comments. I am especially grateful to the referee for their extensive feedback. Much of this work was expanded and edited during the Noncommutative Geometry and D-branes workshop at the Simons Center for Geometry and Physics in December 2011; I thank its participants for many stimulating talks and discussions. I have been supported by the National Science Foundation : grants DMS-0555750 , 0502170 , 1102548 .",
year = "2012",
month = jul,
day = "1",
doi = "10.1016/j.nuclphysb.2012.02.015",
language = "English (US)",
volume = "860",
pages = "167--185",
journal = "Nuclear Physics B",
issn = "0550-3213",
publisher = "Elsevier B.V.",
number = "1",
}