Symmetry Integrability and Geometry Methods and Applications· 2026Q2
A Cohomology Theory of Supercommutative Algebras and Grading-Restricted Vertex Superalgebras
- 0citations
- Q2SCImago
- 2026year
Short summary
A new cohomology theory for grading-restricted vertex superalgebras is constructed, generalizing existing theories and providing a foundation for future research, particularly in the deformation theory of vertex superalgebras.
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Key points
- Introduces a new cohomology theory for grading-restricted vertex superalgebras.
- Includes the construction of a cohomology theory for supercommutative associative algebras.
- Generalizes Yi-Zhi Huang's cohomology theory for vertex algebras.
- Aims to serve as a foundation for future research, particularly deformation theory.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Symmetry Integrability and Geometry Methods and Applications, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics