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THE COMBINATORICS OF TENSOR PRODUCTS OF HIGHER AUSLANDER ALGEBRAS OF TYPE A

Part of: Arithmetic rings and other special rings Special varieties Representation theory of rings and algebras Algebraic combinatorics Homological algebra

Published online by Cambridge University Press:  29 July 2020

JORDAN MCMAHON  and
NICHOLAS J. WILLIAMS
JORDAN MCMAHON
Affiliation:
Universität Graz, Heinrichstrasse 36, A-8010 Graz, Austria, e-mail: jordanmcmahon37@gmail.com
NICHOLAS J. WILLIAMS
Affiliation:
School of Mathematics and Actuarial Science, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom, e-mail: njw40@le.ac.uk
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Abstract

We consider maximal non-l-intertwining collections, which are a higher-dimensional version of the maximal non-crossing collections which give clusters of Plücker coordinates in the Grassmannian coordinate ring, as described by Scott. We extend a method of Scott for producing such collections, which are related to tensor products of higher Auslander algebras of type A. We show that a higher preprojective algebra of the tensor product of two d-representation-finite algebras has a d-precluster-tilting subcategory. Finally, we relate mutations of these collections to a form of tilting for these algebras.

MSC classification

Primary: 05E10: Combinatorial aspects of representation theory
Secondary: 13F60: Cluster algebras 14M15: Grassmannians, Schubert varieties, flag manifolds 16G70: Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers 18G05: Projectives and injectives
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 3 , September 2021 , pp. 526 - 546
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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