WHICH CANONICAL ALGEBRAS ARE DERIVED EQUIVALENT TO INCIDENCE ALGEBRAS OF POSETS? (708)
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BibTeX
@MISC{Ladkani708whichcanonical,
author = {Sefi Ladkani},
title = {WHICH CANONICAL ALGEBRAS ARE DERIVED EQUIVALENT TO INCIDENCE ALGEBRAS OF POSETS?},
year = {708}
}
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Abstract
Abstract. We give a full description of all the canonical algebras over an algebraically closed field that are derived equivalent to incidence algebras of finite posets. These are the canonical algebras whose number of weights is either 2 or 3. This note concerns the characterization of the canonical algebras over an algebraically closed field that are derived equivalent to incidence algebras of finite partially ordered sets (posets), expressed in the following theorem. Theorem. Let Λ be a canonical algebra of type (p,λ) over an algebraically closed field. Then Λ is derived equivalent to an incidence algebra of a poset if and only if the number of weights of p is either 2 or 3. This theorem can be interpreted both geometrically and algebraically. From a geometric viewpoint, by considering modules over incidence algebras as sheaves over finite spaces [8] and using the derived equivalence between the categories of modules over a canonical algebra and coherent sheaves over a weighted projective line [3], we are able to obtain explicit derived
