Higher zigzag algebras

Grant, Joseph (2019) Higher zigzag algebras. Documenta Mathematica, 24. pp. 749-814. ISSN 1431-0643

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Abstract

Given a Koszul algebra of finite global dimension we define its higher zigzag algeba as a twisted trivial extension of the Koszul dual. If our original algebra is the path algebra of a tree-type quiver, this construction recovers the zigzag algebras of Huerfano-Khovanov. We study examples of higher zigzag algebras coming from Iyama’s type A higher representation finite algebras, give their presentations by quivers and relations, and describe relations between spherical twists acting on their derived categories. We connect this to the McKay correspondence in higher dimensions: if G is a finite abelian subgroup of SLd+1 then these relations occur between spherical twists for G-equivariant sheaves on affine (d + 1)-space. 2010 Mathematics Subject Classification: 16. Associative rings and algebras; 18. Category theory, homological algebra; 14. Algebraic geometry

Item Type: Article
Uncontrolled Keywords: trivial extension,braid group action,spherical twist,quiver,derived category,koszul algebra,cluster tilting,equivariant sheaves
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 21 May 2019 10:30
Last Modified: 18 Mar 2020 03:14
URI: https://ueaeprints.uea.ac.uk/id/eprint/71081
DOI: 10.25537/dm.2019v24.749-814

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