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2016 Lifting preprojective algebras to orders and categorifying partial flag varieties
Laurent Demonet, Osamu Iyama
Algebra Number Theory 10(7): 1527-1579 (2016). DOI: 10.2140/ant.2016.10.1527


We describe a categorification of the cluster algebra structure of multihomogeneous coordinate rings of partial flag varieties of arbitrary Dynkin type using Cohen–Macaulay modules over orders. This completes the categorification of Geiss, Leclerc and Schröer by adding the missing coefficients. To achieve this, for an order A and an idempotent e A, we introduce a subcategory CMeA of CMA and study its properties. In particular, under some mild assumptions, we construct an equivalence of exact categories (CMeA)[Ae]SubQ for an injective B-module Q, where B := A(e). These results generalize work by Jensen, King and Su concerning the cluster algebra structure of the Grassmannian Grm(n).


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Laurent Demonet. Osamu Iyama. "Lifting preprojective algebras to orders and categorifying partial flag varieties." Algebra Number Theory 10 (7) 1527 - 1579, 2016.


Received: 25 September 2015; Revised: 26 April 2016; Accepted: 13 June 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1383.16019
MathSciNet: MR3554240
Digital Object Identifier: 10.2140/ant.2016.10.1527

Primary: 16G30
Secondary: 13F60, 16G10, 16G50, 18E10, 18E30

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.10 • No. 7 • 2016
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