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On radicals in differential invariants: global theory vs moving frames
Abstract
The classical technique of moving frames allows to effectively compute differential invariants of group actions. A standard observation is that the expressions of differential invariants contain radicals and more complicated algebraic functions, however the global Lie-Tresse theorem claims that for algebraic pseudogroup actions the algebra of differential invariants is generated by rational functions in jet variables. Here, we explain this apparent contradiction and illustrate it in a few well-elaborated examples. Constructively, our result gives a method to algorithmically compute global differential invariants.
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BibTeX
@misc{kruglikov2026radicals,
title = {{On radicals in differential invariants: global theory vs moving frames}},
author = {Boris Kruglikov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.04080},
eprint = {2609.04080},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04080},
}
RIS
TY - UNPB
TI - On radicals in differential invariants: global theory vs moving frames
AU - Boris Kruglikov
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2609.04080
UR - https://arxiv.org/abs/2609.04080
AB - The classical technique of moving frames allows to effectively compute differential invariants of group actions. A standard observation is that the expressions of differential invariants contain radicals and more complicated algebraic functions, however the global Lie-Tresse theorem claims that for algebraic pseudogroup actions the algebra of differential invariants is generated by rational functions in jet variables. Here, we explain this apparent contradiction and illustrate it in a few well-elaborated examples. Constructively, our result gives a method to algorithmically compute global differential invariants.
ER -