Representation theory of three-dimensional Sklyanin algebras

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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.

Original languageEnglish (US)
Pages (from-to)167-185
Number of pages19
JournalNuclear Physics B
Volume860
Issue number1
DOIs
StatePublished - Jul 1 2012

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ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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