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PreprintCC BY 4.0arXiv

Conjugation Differential Invariants of SL2(𝔽q) on trace-free matrices

  • Jonathan Elmer
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Abstract

Let q=pk be prime power, let F= 𝔽q and let V be the vector space of 2 by 2 matrices over F with trace zero. Let G = SL2(F). Then G acts on V via conjugation. Let Ω= S(V*) ⊗ Λ(V*) be the algebra of differential forms on V. A minimal generating set for ΩG when q=3 was computed by the author and Meyer. In this article we compute a minimal generating set for ΩG for all q.

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Cite

BibTeXRIS
BibTeX
@misc{elmer2026conjugation,
  title = {{Conjugation Differential Invariants of $\mathrmSL_2(\mathbbF_q)$ on trace-free matrices}},
  author = {Jonathan Elmer},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.28195},
  eprint = {2609.28195},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28195},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Conjugation Differential Invariants of SL_2(𝔽_q) on trace-free matrices
AU  - Jonathan Elmer
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.28195
UR  - https://arxiv.org/abs/2609.28195
AB  - Let q=p^k be prime power, let F= 𝔽_q and let V be the vector space of 2 by 2 matrices over F with trace zero. Let G = SL_2(F). Then G acts on V via conjugation. Let Ω= S(V^*) ⊗ Λ(V^*) be the algebra of differential forms on V. A minimal generating set for Ω^G when q=3 was computed by the author and Meyer. In this article we compute a minimal generating set for Ω^G for all q.
ER  -