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PreprintCC BY 4.0arXiv

AV-modules on affine algebraic groups

  • Yuly Billig
  • Colin Ingalls
Open at sourcePDFDOICite

Abstract

We study AV-modules on an affine algebraic group G, that is, modules that admit compatible actions of the algebra of regular functions on G and the Lie algebra of vector fields. A central role in this theory is played by the Lie algebra of jets of vector fields. Our main result is the Decomposition Theorem for the Lie algebra of jets of vector fields. We apply the Decomposition Theorem to describe differentiable AV-modules on G.

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Cite

BibTeXRIS
BibTeX
@misc{billig2026avmodules,
  title = {{$AV$-modules on affine algebraic groups}},
  author = {Yuly Billig and Colin Ingalls},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00905},
  eprint = {2611.00905},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00905},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - AV-modules on affine algebraic groups
AU  - Yuly Billig
AU  - Colin Ingalls
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00905
UR  - https://arxiv.org/abs/2611.00905
AB  - We study AV-modules on an affine algebraic group G, that is, modules that admit compatible actions of the algebra of regular functions on G and the Lie algebra of vector fields. A central role in this theory is played by the Lie algebra of jets of vector fields. Our main result is the Decomposition Theorem for the Lie algebra of jets of vector fields. We apply the Decomposition Theorem to describe differentiable AV-modules on G.
ER  -