$n$-APR tilting and $\tau$-mutations

Jin Yun Guo; Cong Xiao

$n$-APR tilting and $\tau$-mutations

Representation Theory 2020-06-19 v2

Authors: Jin Yun Guo , Cong Xiao

Abstract

APR tilts for path algebra $kQ$ can be realized as the mutation of the quiver $Q$ in $\mathbb Z Q$ with respect to the translation. In this paper, we show that we have similar results for the quadratic dual of truncations of $n$ -translation algebras, that is, under certain condition, the $n$ -APR tilts of such algebras are realized as $\tau$ -mutations.For the dual $\tau$ -slice algebras with bound quiver $Q^{\perp}$ , we show that their iterated $n$ -APR tilts are realized by the iterated $\tau$ -mutations in $\mathbb Z|{n-1}Q^{\perp}$ .

Cite

@article{arxiv.1901.08465,
  title  = {$n$-APR tilting and $\tau$-mutations},
  author = {Jin Yun Guo and Cong Xiao},
  journal= {arXiv preprint arXiv:1901.08465},
  year   = {2020}
}

Comments

This paper is a extended and generalized version of the results concerning $n$-APR tilts in '$\tau$-slice algebras of $n$-translation algebras and quasi $n$-Fano algebras, arXiv:1707.01393, which is discontinued

$n$-APR tilting and $\tau$-mutations

Abstract

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