n-APR tilting and τ-mutations

2019/01/23 by Guo, Jin Yun, Xiao, Cong
#16G20 #16G70 #16S37 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1901.08465

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 τ-mutations.For the dual τ-slice algebras with bound quiver Q^⊥, we show that their iterated n-APR tilts are realized by the iterated τ-mutations in \mathbb Z|n-1Q^⊥.

Related

• Reduction Techniques to Identify Connected Components of Mutation Quivers
• τ-slice algebras of n-translation algebras and quasi n-Fano algebras
• APR tilting modules and graded quivers with potential
• A combinatorial procedure for tilting mutation
• Derived equivalences between symmetric special biserial algebras