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PreprintCC BY-NC-ND 4.0arXiv

Realizable Cohomology Classes of Dihedral and Generalized Quaternion Groups

  • Sutirtha Datta
  • Jyotirmoy Ganguly
  • Rohit Joshi
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Abstract

We compute the Chern classes of irreducible representations for the dihedral groups D2n and the generalized quaternion groups Q2n. Utilizing these computations, we investigate whether every even-dimensional class in the integral group cohomology of these families can be realized as a Chern class of some complex representation. It turns out that this realizability question answers in the affirmative for the generalized quaternion groups. In contrast, it turns out that the answer for dihedral groups is erratic.

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Cite

BibTeXRIS
BibTeX
@misc{datta2026realizable,
  title = {{Realizable Cohomology Classes of Dihedral and Generalized Quaternion Groups}},
  author = {Sutirtha Datta and Jyotirmoy Ganguly and Rohit Joshi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32680},
  eprint = {2610.32680},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32680},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Realizable Cohomology Classes of Dihedral and Generalized Quaternion Groups
AU  - Sutirtha Datta
AU  - Jyotirmoy Ganguly
AU  - Rohit Joshi
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32680
UR  - https://arxiv.org/abs/2610.32680
AB  - We compute the Chern classes of irreducible representations for the dihedral groups D_2n and the generalized quaternion groups Q_2^n. Utilizing these computations, we investigate whether every even-dimensional class in the integral group cohomology of these families can be realized as a Chern class of some complex representation. It turns out that this realizability question answers in the affirmative for the generalized quaternion groups. In contrast, it turns out that the answer for dihedral groups is erratic.
ER  -