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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Preprojective Algebras, Singularity Categories and Orthogonal Decompositions
verfasst von : Claire Amiot
Erschienen in: Algebras, Quivers and Representations
Verlag: Springer Berlin Heidelberg
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Abstract
In this note we use results of Minamoto (Int. Math. Res. Not., 67–101, 2012) and Amiot-Iyama-Reiten (arXiv:1104.3658, 2011) to construct an embedding of the graded singularity category of certain graded Gorenstein algebras into the derived category of coherent sheaves over its projective scheme. These graded algebras are constructed using the preprojective algebras of d-representation infinite algebras as defined by Herschend-Iyama-Oppermann in arXiv:1205.1272 (2012). We relate this embedding to the construction of a semi-orthogonal decomposition of the derived category of coherent sheaves over the projective scheme of a Gorenstein algebra of parameter 1 described by Orlov in (Algebra, arithmetic, and geometry: in honor of Yu. I. Manin, vol. II, pp. 503–531, 2009).