Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 48 min ago
PreprintCC BY-SA 4.0arXiv

Cotensor decompositions for comodules over graded vertex operator coalgebras

  • Hao Wang
Open at sourcePDFDOICite

Abstract

Let V be a graded vertex operator coalgebra and π’ž the category of admissible V-comodules. We first give the construction of contragredient comodule of an admissible V-comodule. We then introduce cointertwining operators among admissible V-comodules. Using cointertwining operators, we define the cotensor decomposition of an admissible V-comodule by a universal property. Finally, we prove that the complexified Grothendieck group 𝕂[π’ž]=β„‚βŠ—β„€K[π’ž] is a cocommutative coassociative coalgebra. Moreover, this coalgebra is naturally dual to the fusion algebra of the category of admissible modules over the dual vertex operator algebra V'.

Related

  1. Ext-groups of graded comodules
    Andrew Salch
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  2. Graded bimodules over split group algebras: stabilizers and Peirce decompositions
    Felipe de Mattos Chafik Hindi, Waldeck Schutzer
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Affine and Lattice Structures in Regular β„•-Graded Vertex Operator Algebras with Gorenstein V0
    Gaywalee Yamskulna
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Higher Spherical Scissors Congruence II: Comodules
    Inbar Klang, Josefien Kuijper, Cary Malkiewich +2
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  5. Quasi-quantum groups arising from cotensor coquasi-Hopf algebras
    Jing Yu, Xiangjun Zhen
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{wang2026cotensor,
  title = {{Cotensor decompositions for comodules over graded vertex operator coalgebras}},
  author = {Hao Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20894},
  eprint = {2609.20894},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20894},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Cotensor decompositions for comodules over graded vertex operator coalgebras
AU  - Hao Wang
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20894
UR  - https://arxiv.org/abs/2609.20894
AB  - Let V be a graded vertex operator coalgebra and π’ž the category of admissible V-comodules. We first give the construction of contragredient comodule of an admissible V-comodule. We then introduce cointertwining operators among admissible V-comodules. Using cointertwining operators, we define the cotensor decomposition of an admissible V-comodule by a universal property. Finally, we prove that the complexified Grothendieck group 𝕂[π’ž]=β„‚βŠ—_β„€K[π’ž] is a cocommutative coassociative coalgebra. Moreover, this coalgebra is naturally dual to the fusion algebra of the category of admissible modules over the dual vertex operator algebra V'.
ER  -