The dg Leavitt path algebra, singular Yonda category and singularity category

Abstract: We prove that, for any finite dimensional algebra given by a quiver with relations, its dg singularity category is quasi-equivalent to the perfect dg derived category of the dg Leavitt path algebra of its radical quiver. This result might be viewed as a deformation of the known description of the dg singularity category of a radical-square-zero algebra in terms of a Leavitt path algebra. The main ingredient is a new dg enhancement of the singularity category, namely the singular Yoneda dg category, which is obtained by a new strict dg localization inverting a natural transformation. This is joint with Zhengfang Wang.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides )

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