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PreprintCC BY 4.0arXiv

The commuting scheme of g2

  • Pallav Goyal
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Abstract

We study the commuting scheme of the exceptional Lie algebra g2 via computational methods. Over a field of characteristic zero, we show that the commuting scheme of g2 is reduced, Cohen-Macaulay and normal. Our computations give an explicit homogeneous system of parameters, determine the Hilbert series and degree, identify the first syzygies of the commuting ideal and show that it is not Gorenstein. We extend some of the above results to positive characteristic.

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Cite

BibTeXRIS
BibTeX
@misc{goyal2026commuting,
  title = {{The commuting scheme of $\mathfrakg_2$}},
  author = {Pallav Goyal},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05018},
  eprint = {2610.05018},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05018},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The commuting scheme of g_2
AU  - Pallav Goyal
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.05018
UR  - https://arxiv.org/abs/2610.05018
AB  - We study the commuting scheme of the exceptional Lie algebra g_2 via computational methods. Over a field of characteristic zero, we show that the commuting scheme of g_2 is reduced, Cohen-Macaulay and normal. Our computations give an explicit homogeneous system of parameters, determine the Hilbert series and degree, identify the first syzygies of the commuting ideal and show that it is not Gorenstein. We extend some of the above results to positive characteristic.
ER  -