Koszul duality for finite-dimensional absolutely Koszul algebras

@misc{bouhada2026koszul,
  title = {{Koszul duality for finite-dimensional absolutely Koszul algebras}},
  author = {A. M. Bouhada},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06768},
  eprint = {2609.06768},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06768},
}

TY  - UNPB
TI  - Koszul duality for finite-dimensional absolutely Koszul algebras
AU  - A. M. Bouhada
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.06768
UR  - https://arxiv.org/abs/2609.06768
AB  - Let Λ be a finite-dimensional Koszul algebra. Using a description of the linear part of minimal projective resolutions in terms of Koszul duality, we prove that Λ is absolutely Koszul if and only if its Koszul dual Λ^! is graded left co-coherent. We further show that an absolutely Koszul algebra of finite global linearity defect has finite graded finitistic dimension. Finally, we refine Koszul duality for finite-dimensional absolutely Koszul algebras. As a further application, we answer a question of Green et al.~\cite{12} by means of the Koszul dual algebra.
ER  -