Signature matrices of membranes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915802107609088 |
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| author | Lotter, Felix Schmitz, Leonard |
| author_facet | Lotter, Felix Schmitz, Leonard |
| contents | The signature of a membrane is a sequence of tensors whose entries are iterated integrals. We study algebraic properties of membrane signatures, with a focus on signature matrices of polynomial and piecewise bilinear membranes. Generalizing known results for path signatures, we show that the two families of membranes admit the same set of signature matrices and we examine the corresponding affine varieties. In particular, we prove that there are no algebraic relations on signature matrices of membranes, in contrast to the path case. We complement our results by a linear time algorithm for the computation of signature tensors for piecewise bilinear membranes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11996 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Signature matrices of membranes Lotter, Felix Schmitz, Leonard Algebraic Geometry Rings and Algebras 60L10, 14Q15, 13P25 The signature of a membrane is a sequence of tensors whose entries are iterated integrals. We study algebraic properties of membrane signatures, with a focus on signature matrices of polynomial and piecewise bilinear membranes. Generalizing known results for path signatures, we show that the two families of membranes admit the same set of signature matrices and we examine the corresponding affine varieties. In particular, we prove that there are no algebraic relations on signature matrices of membranes, in contrast to the path case. We complement our results by a linear time algorithm for the computation of signature tensors for piecewise bilinear membranes. |
| title | Signature matrices of membranes |
| topic | Algebraic Geometry Rings and Algebras 60L10, 14Q15, 13P25 |
| url | https://arxiv.org/abs/2409.11996 |