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arXiv · 1602.05646

Recollements, sinks elimination and Leavitt path algebras

Roozbeh Hazrat·Ju Huang
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Abstract

For Leavitt path algebras, we show that whereas removing sources from a graph produces a Morita equivalence, removing sinks gives rise to a recollement situation. In general, we show that for a graph $E$ and a finite hereditary subset $H$ of $E^0$ there is a recollement $$\xymatrix{ L_K(E/\overline H) \rModd \ar[r] & \ar@<3pt>[l] \ar@<-3pt>[l] L_K(E) \rModd \ar[r] & \ar@<3pt>[l] \ar@<-3pt>[l] L_K(E_H) \rModd .}$$ We record several corollaries.

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Roozbeh Hazrat, Ju Huang. 2016-02-18. Recollements, sinks elimination and Leavitt path algebras. https://arxiv.org/abs/1602.05646

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