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Abstract:
Sklyanin algebras play an important role in the study of physical phenomenon. We will first review techniques of Artin-Tate-van den Bergh (ATV) that describe the ring-theoretic and homological behavior of these structures. In particular, we highlight the significance of twisted homogeneous coordinate rings.
Moreover the focus of the talk is to introduce a generalized twisted homogeneous coordinate ring P associated to a degenerate version of the three-dimensional Sklyanin algebra. The surprising geometry of these algebras yields an analogue to a result of ATV; namely that P is a factor of the corresponding degenerate Sklyanin algebra.
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