Skip to content
DraconiticResearch
Search Sources API
190,869 studies31 sourcesUpdated 37 min ago
PreprintCC BY 4.0arXiv

Diassociative conformal algebras and their deformation cohomology

  • Anupam Sahoo
  • Apurba Das
Open at sourcePDFDOICite

Abstract

In this paper, we introduce diassociative conformal algebras that unify both associative conformal algebras and diassociative algebras. We show that the category of diassociative conformal algebras is equivalent to the category of equivalence classes of formal distribution diassociative algebras. By employing its Maurer-Cartan characterization, we then define the cohomology of a diassociative conformal algebra and show that it carries a Gerstenhaber algebra structure. Our cohomology can be used to study deformations and extensions of the structure. Finally, we define averaging operators on associative conformal algebras and find their close relations with diassociative conformal algebras.

Related

  1. Deformation of affine structures and the cohomology of Koszul-Vinberg algebras on the lie groups SO(2), H3(R) and Galilei group SGal(3)
    Prosper R. Mama Assandje, R. Nimpa Pefoukeu, Michel B. Djiadeu Ngaha +2
    arXivPreprintCC0Full textGeometry & topologyarXiv
  2. Deformation maps on quasi-twilled Lie conformal algebras
    Taoufik Chtioui, Sami Mabrouk, Abdenacer Makhlouf
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. BV structure on the Hochschild cohomology of Liu-Schulz algebras in characteristic two
    Artur Tursunbaev
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. On motivic cohomology of commutative C*-algebras
    Ko Aoki
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv
  5. A Cohomology Theory of Supercommutative Algebras and Grading-Restricted Vertex Superalgebras
    Paul Johnson, Fei Qi
    Symmetry, Integrability and Geometry: Methods and ApplicationsPeer-reviewedCC BY-SA 4.0Mathematical physicsCrossref

Cite

BibTeXRIS
BibTeX
@misc{sahoo2026diassociative,
  title = {{Diassociative conformal algebras and their deformation cohomology}},
  author = {Anupam Sahoo and Apurba Das},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17441},
  eprint = {2609.17441},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17441},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Diassociative conformal algebras and their deformation cohomology
AU  - Anupam Sahoo
AU  - Apurba Das
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17441
UR  - https://arxiv.org/abs/2609.17441
AB  - In this paper, we introduce diassociative conformal algebras that unify both associative conformal algebras and diassociative algebras. We show that the category of diassociative conformal algebras is equivalent to the category of equivalence classes of formal distribution diassociative algebras. By employing its Maurer-Cartan characterization, we then define the cohomology of a diassociative conformal algebra and show that it carries a Gerstenhaber algebra structure. Our cohomology can be used to study deformations and extensions of the structure. Finally, we define averaging operators on associative conformal algebras and find their close relations with diassociative conformal algebras.
ER  -