A note on free divergence-free vector fields
Operator Algebras
2024-01-08 v2 Rings and Algebras
Abstract
We exhibit an orthonormal basis of cyclic gradients and a (non-orthogonal) basis of the homogeneous free divergence-free vector field on the full Fock space and determine the dimension of Voiculescu's free divergence-free vector field of degree k or less. Moreover, we also give a concrete formula for the orthogonal projection onto the space of cyclic gradients as well as the free Leray projection.
Keywords
Cite
@article{arxiv.2311.15550,
title = {A note on free divergence-free vector fields},
author = {Hyuga Ito and Akihiro Miyagawa},
journal= {arXiv preprint arXiv:2311.15550},
year = {2024}
}
Comments
8 pages. We improved the introduction and added one remark in the last part. We also added examples of vectors in the free divergence-free vector field, inspired by the classical case