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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.06691 |
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| _version_ | 1866909071439822848 |
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| author | Schmitz, Leonard Tapia, Nikolas |
| author_facet | Schmitz, Leonard Tapia, Nikolas |
| contents | Signature transforms have recently been extended to data indexed by two and more parameters. With free Lyndon generators, ideas from $\mathbf{B}_\infty$-algebras and a novel two-parameter Hoffman exponential, we provide three classes of isomorphisms between the underlying two-parameter shuffle and quasi-shuffle algebras. In particular, we provide a Hopf algebraic connection to the (classical, one-parameter) shuffle algebra over the extended alphabet of connected matrix compositions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06691 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Free generators and Hoffman's isomorphism for the two-parameter shuffle algebra Schmitz, Leonard Tapia, Nikolas Rings and Algebras Signature transforms have recently been extended to data indexed by two and more parameters. With free Lyndon generators, ideas from $\mathbf{B}_\infty$-algebras and a novel two-parameter Hoffman exponential, we provide three classes of isomorphisms between the underlying two-parameter shuffle and quasi-shuffle algebras. In particular, we provide a Hopf algebraic connection to the (classical, one-parameter) shuffle algebra over the extended alphabet of connected matrix compositions. |
| title | Free generators and Hoffman's isomorphism for the two-parameter shuffle algebra |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2401.06691 |