Batalin-Vilkovisky algebras from Ševera bicomplexes
Abstract
A Ševera bicomplex is a bicomplex (M,d0,d1) whose differentials di are Grothendieck differential operators of order ≤ i with respect to a given A-module structure on M, where A is a graded commutative algebra. One also requires that (M,d0) admits a contracting homotopy K that is a differential operator of the same order as d0. Under suitable assumptions, the differential d2 of the second page of the spectral sequence associated with (M,d0,d1) is a Batalin-Vilkovisky operator on E2, so that when E2 is a free rank 1 A-module, the graded commutative algebra structure of A is enhanced to a Gerstenhaber algebra structure, and the choice of a d2-closed basis element for E2 further enhances this to a Batalin-Vilkovisky algebra structure. The prototypical example of this construction is Ševera's description of the Batalin--Vilkovisky algebra structure on the algebra of smooth functions of an odd symplectic manifold. Throughout the whole article we look at Batalin-Vilkovisky algebras through the lenses of Cartan calculus. Indications of a generalization to derived Cartan calculus are briefly discussed in the concluding section.
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BibTeX
@misc{boffo2026batalinvilkovisky,
title = {{Batalin-Vilkovisky algebras from Ševera bicomplexes}},
author = {Eugenia Boffo and Domenico Fiorenza},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24781},
eprint = {2609.24781},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24781},
}
RIS
TY - UNPB
TI - Batalin-Vilkovisky algebras from Ševera bicomplexes
AU - Eugenia Boffo
AU - Domenico Fiorenza
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24781
UR - https://arxiv.org/abs/2609.24781
AB - A Ševera bicomplex is a bicomplex (M,d_0,d_1) whose differentials d_i are Grothendieck differential operators of order ≤ i with respect to a given A-module structure on M, where A is a graded commutative algebra. One also requires that (M,d_0) admits a contracting homotopy K that is a differential operator of the same order as d_0. Under suitable assumptions, the differential d_2 of the second page of the spectral sequence associated with (M,d_0,d_1) is a Batalin-Vilkovisky operator on E_2, so that when E_2 is a free rank 1 A-module, the graded commutative algebra structure of A is enhanced to a Gerstenhaber algebra structure, and the choice of a d_2-closed basis element for E_2 further enhances this to a Batalin-Vilkovisky algebra structure. The prototypical example of this construction is Ševera's description of the Batalin--Vilkovisky algebra structure on the algebra of smooth functions of an odd symplectic manifold. Throughout the whole article we look at Batalin-Vilkovisky algebras through the lenses of Cartan calculus. Indications of a generalization to derived Cartan calculus are briefly discussed in the concluding section.
ER -