Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 30 min ago
PreprintarXiv licencearXiv

Completing the classification of Hopf superalgebras of dimension up to 10

  • Taiki Shibata
  • Kenichi Shimizu
  • Ryota Wakao
Open at sourcePDFDOICite

Abstract

We introduce a family of semisimple Hopf superalgebras obtained from abelian extensions. Using this family and bosonization, we complete the classification of Hopf superalgebras of dimension up to 10 over an algebraically closed field of characteristic zero. We also determine the duals of the semisimple classes with nonzero odd part and give tables of the complete classification.

Related

  1. Sophus Lie's problem on two-dimensional metrics with projective symmetries: completing the local classification
    Gianni Manno, Vladimir S. Matveev, Filippo Salis
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  2. The algebraic and geometric classification of semi-alternative superalgebras
    Hani Abdelwahab, Ivan Kaygorodov, Roman Lubkov
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. A q-Weyl Freeness Principle for Nichols Algebras and Pointed Hopf Algebras of Square-Free Dimension
    Rongchuan Xiong
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Classification of Rational c=1 Vertex Operator Algebras and Vertex Operator Superalgebras
    Terry Gannon, Brandon C. Rayhaun
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCondensed matterarXiv
  5. The classification of some polynomial maps in dimension three
    Yuan He, Dan Yan
    arXivPreprintCC BY-NC-SA 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{shibata2026completing,
  title = {{Completing the classification of Hopf superalgebras of dimension up to 10}},
  author = {Taiki Shibata and Kenichi Shimizu and Ryota Wakao},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00632},
  eprint = {2611.00632},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00632},
}
RIS
TY  - UNPB
TI  - Completing the classification of Hopf superalgebras of dimension up to 10
AU  - Taiki Shibata
AU  - Kenichi Shimizu
AU  - Ryota Wakao
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00632
UR  - https://arxiv.org/abs/2611.00632
AB  - We introduce a family of semisimple Hopf superalgebras obtained from abelian extensions. Using this family and bosonization, we complete the classification of Hopf superalgebras of dimension up to 10 over an algebraically closed field of characteristic zero. We also determine the duals of the semisimple classes with nonzero odd part and give tables of the complete classification.
ER  -