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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-11-01
|
| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.631/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206182803931136 |
|---|---|
| author | Ito, Hyuga Miyagawa, Akihiro |
| author_facet | Ito, Hyuga Miyagawa, Akihiro |
| author_sort | Ito, Hyuga |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-bfb3a55353294325b651e9745f3401d5 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-bfb3a55353294325b651e9745f3401d52025-02-07T11:26:37ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G121545155410.5802/crmath.63110.5802/crmath.631A note on free divergence-free vector fieldsIto, Hyuga0https://orcid.org/0009-0008-6388-804XMiyagawa, Akihiro1https://orcid.org/0000-0002-2525-5283Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, 464-8602, JapanDepartment of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, 606-8502, Japan; Department of Mathematics, University of California San Diego, La Jolla, CA 92093, USAWe 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.631/Free probabilityFree semi-circular systemFree divergence-free vector fieldsCyclic gradients |
| spellingShingle | Ito, Hyuga Miyagawa, Akihiro A note on free divergence-free vector fields Comptes Rendus. Mathématique Free probability Free semi-circular system Free divergence-free vector fields Cyclic gradients |
| title | A note on free divergence-free vector fields |
| title_full | A note on free divergence-free vector fields |
| title_fullStr | A note on free divergence-free vector fields |
| title_full_unstemmed | A note on free divergence-free vector fields |
| title_short | A note on free divergence-free vector fields |
| title_sort | note on free divergence free vector fields |
| topic | Free probability Free semi-circular system Free divergence-free vector fields Cyclic gradients |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.631/ |
| work_keys_str_mv | AT itohyuga anoteonfreedivergencefreevectorfields AT miyagawaakihiro anoteonfreedivergencefreevectorfields AT itohyuga noteonfreedivergencefreevectorfields AT miyagawaakihiro noteonfreedivergencefreevectorfields |