Derived equivalences of self-injective 2-Calabi–Yau tilted algebras

TY - JOUR

T1 - Derived equivalences of self-injective 2-Calabi–Yau tilted algebras

AU - Kortegaard, Anders S.

N1 - Publisher Copyright: © 2024 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

PY - 2024/3

Y1 - 2024/3

N2 - Consider a (Formula presented.) -linear Frobenius category (Formula presented.) such that the corresponding stable category (Formula presented.) is 2-Calabi–Yau, Hom-finite with split idempotents. Let (Formula presented.) be maximal rigid objects with self-injective endomorphism algebras. We will show that their endomorphism algebras (Formula presented.) and (Formula presented.) are derived equivalent. Furthermore, we will give a description of the two-sided tilting complex that induces this derived equivalence.

AB - Consider a (Formula presented.) -linear Frobenius category (Formula presented.) such that the corresponding stable category (Formula presented.) is 2-Calabi–Yau, Hom-finite with split idempotents. Let (Formula presented.) be maximal rigid objects with self-injective endomorphism algebras. We will show that their endomorphism algebras (Formula presented.) and (Formula presented.) are derived equivalent. Furthermore, we will give a description of the two-sided tilting complex that induces this derived equivalence.

U2 - 10.1112/blms.12982

DO - 10.1112/blms.12982

M3 - Journal article

AN - SCOPUS:85181468434

SN - 0024-6093

VL - 56

SP - 1071

EP - 1094

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 3

ER -