PreprintCC BY 4.0arXiv
Reciprocity for projective and injective direct summands
Abstract
A reciprocity between multiplicities of projective direct summands for modular group algebras has been known for decades. Recently, the first author extended it to finite-dimensional symmetric algebras. We further generalize the reciprocity theorem to arbitrary finite-dimensional algebras by establishing a tensor-hom adjunction for stable and costable categories.
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BibTeX
@misc{koshitani2026reciprocity,
title = {{Reciprocity for projective and injective direct summands}},
author = {Shigeo Koshitani and Taro Sakurai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11276},
eprint = {2610.11276},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11276},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reciprocity for projective and injective direct summands
AU - Shigeo Koshitani
AU - Taro Sakurai
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11276
UR - https://arxiv.org/abs/2610.11276
AB - A reciprocity between multiplicities of projective direct summands for modular group algebras has been known for decades. Recently, the first author extended it to finite-dimensional symmetric algebras. We further generalize the reciprocity theorem to arbitrary finite-dimensional algebras by establishing a tensor-hom adjunction for stable and costable categories.
ER -