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A note on free divergence-free vector fields

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.

preprint2024arXivOpen access
Hyuga ItoAkihiro Miyagawa
math.OAmath.RA
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Hyuga ItoAkihiro Miyagawa

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