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PreprintCC BY 4.0arXiv

Diagonalizable modular derivations on bigraded Poisson spaces and Koszul duality

  • Ruobing Chen
  • Di Zhang
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Abstract

For two bigraded spaces km||n and kn∧ m equipped with appropriate quadratic Poisson structures, Koszul duality identifies the mixed Poisson differential calculi and, in the unimodular case, their Poisson cohomologies as Batalin--Vilkovisky algebras. In the current paper we prove that Koszul duality induces an isomorphism of Batalin--Vilkovisky algebras between their Poisson cohomologies when the modular derivation of one algebra is diagonalizable, including non-unimodular cases.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026diagonalizable,
  title = {{Diagonalizable modular derivations on bigraded Poisson spaces and Koszul duality}},
  author = {Ruobing Chen and Di Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08091},
  eprint = {2610.08091},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08091},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Diagonalizable modular derivations on bigraded Poisson spaces and Koszul duality
AU  - Ruobing Chen
AU  - Di Zhang
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08091
UR  - https://arxiv.org/abs/2610.08091
AB  - For two bigraded spaces k^m||n and k^n∧ m equipped with appropriate quadratic Poisson structures, Koszul duality identifies the mixed Poisson differential calculi and, in the unimodular case, their Poisson cohomologies as Batalin--Vilkovisky algebras. In the current paper we prove that Koszul duality induces an isomorphism of Batalin--Vilkovisky algebras between their Poisson cohomologies when the modular derivation of one algebra is diagonalizable, including non-unimodular cases.
ER  -