Simplicial complexes and tilting theory for Brauer tree algebras

Hideto Asashiba, Yuya Mizuno, Ken Nakashima

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We study 2-term tilting complexes of Brauer tree algebras in terms of simplicial complexes. We show the symmetry and convexity of the lattice polytope corresponding to the simplicial complex of 2-term tilting complexes. Via a geometric interpretation of derived equivalences, we show that the f-vector of the simplicial complexes of Brauer tree algebras only depends on the number of the edges of the Brauer trees and hence it is a derived invariant. In particular, this result implies that the number of 2-term tilting complexes, which is in bijection with support τ-tilting modules, is a derived invariant. Moreover, we apply our result to the enumeration problem of Coxeter-biCatalan combinatorics.

Original languageEnglish
Pages (from-to)119-153
Number of pages35
JournalJournal of Algebra
Volume551
DOIs
Publication statusPublished - Jun 1 2020
Externally publishedYes

Keywords

  • 2-term tilting complexes
  • Brauer tree algebras
  • Derived invariants
  • Simplicial complexes

ASJC Scopus subject areas

  • Algebra and Number Theory

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