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Peer-reviewedCC BY-SA 4.0Symmetry, Integrability and Geometry: Methods and Applications

A Cohomology Theory of Supercommutative Algebras and Grading-Restricted Vertex Superalgebras

  • Paul Johnson1
  • Fei Qi2
  1. 1University of Denver, USA
  2. 2Sun Yat-Sen University, P.R. China
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Abstract

This paper constructs the cohomology theory for grading-restricted vertex superalgebras, generalizing Yi-Zhi Huang's cohomology theory of grading-restricted vertex algebras. To simplify the discussion, motivate the construction, and make it easier for the reader to understand the technical points, we also include the construction of the cohomology theory of supercommutative associative algebras, a generalization of the Harrison cohomology theory of a commutative algebra that has not been explicitly written down. The paper will serve as the foundation for many subsequent studies, especially the deformation theory of vertex superalgebras.

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Cite

BibTeXRIS
BibTeX
@article{johnson2026cohomology,
  title = {{A Cohomology Theory of Supercommutative Algebras and Grading-Restricted Vertex Superalgebras}},
  author = {Paul Johnson and Fei Qi},
  journal = {Symmetry, Integrability and Geometry: Methods and Applications},
  year = {2026},
  month = oct,
  doi = {10.3842/sigma.2026.103},
  url = {https://sigma-journal.com/2026/103/},
  note = {CC BY-SA 4.0},
}
RIS
TY  - JOUR
TI  - A Cohomology Theory of Supercommutative Algebras and Grading-Restricted Vertex Superalgebras
AU  - Paul Johnson
AU  - Fei Qi
PY  - 2026
DA  - 2026/10/29
JO  - Symmetry, Integrability and Geometry: Methods and Applications
DO  - 10.3842/sigma.2026.103
UR  - https://sigma-journal.com/2026/103/
AB  - This paper constructs the cohomology theory for grading-restricted vertex superalgebras, generalizing Yi-Zhi Huang's cohomology theory of grading-restricted vertex algebras. To simplify the discussion, motivate the construction, and make it easier for the reader to understand the technical points, we also include the construction of the cohomology theory of supercommutative associative algebras, a generalization of the Harrison cohomology theory of a commutative algebra that has not been explicitly written down. The paper will serve as the foundation for many subsequent studies, especially the deformation theory of vertex superalgebras.
SN  - 1815-0659
ER  -