Vol. 10, No. 7, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 9, 1589–1766
Issue 8, 1403–1587
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
Lifting preprojective algebras to orders and categorifying partial flag varieties

Laurent Demonet and Osamu Iyama

Vol. 10 (2016), No. 7, 1527–1579
Abstract

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).

Keywords
orders, Cohen–Macaulay modules, finite-dimensional algebras, preprojective algebras, categorification, cluster algebras, partial flag varieties, exact categories
Mathematical Subject Classification 2010
Primary: 16G30
Secondary: 13F60, 16G10, 16G50, 18E10, 18E30
Milestones
Received: 25 September 2015
Revised: 26 April 2016
Accepted: 13 June 2016
Published: 27 September 2016
Authors
Laurent Demonet
Graduate School of Mathematics
Nagoya University
Furocho
Chikusaku
Nagoya 464-8602
Japan
Osamu Iyama
Graduate School of Mathematics
Nagoya University
Furocho
Chikusaku
Nagoya 464-8602
Japan