On Symmetries of Finite Geometries
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916378951286784 |
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| author | Knill, Oliver |
| author_facet | Knill, Oliver |
| contents | The isospectral set of the Dirac matrix D=d+d* consists of orthogonal Q for which Q* D Q is an equivalent Dirac matrix. It can serve as the symmetry of a finite geometry G. The symmetry is a subset of the orthogonal group or unitary group and isospectral Lax deformations produce commuting flows d/dt D=[B(g(D)),D] on this symmetry space. In this note, we remark that like in the Toda case, D_t=Q_t* D_0 Q_t with exp(-t g(D))=Q_t R_t solves the Lax system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13973 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Symmetries of Finite Geometries Knill, Oliver Exactly Solvable and Integrable Systems Discrete Mathematics Mathematical Physics Dynamical Systems 68RXX 37JXX The isospectral set of the Dirac matrix D=d+d* consists of orthogonal Q for which Q* D Q is an equivalent Dirac matrix. It can serve as the symmetry of a finite geometry G. The symmetry is a subset of the orthogonal group or unitary group and isospectral Lax deformations produce commuting flows d/dt D=[B(g(D)),D] on this symmetry space. In this note, we remark that like in the Toda case, D_t=Q_t* D_0 Q_t with exp(-t g(D))=Q_t R_t solves the Lax system. |
| title | On Symmetries of Finite Geometries |
| topic | Exactly Solvable and Integrable Systems Discrete Mathematics Mathematical Physics Dynamical Systems 68RXX 37JXX |
| url | https://arxiv.org/abs/2408.13973 |