An extension of the linearized double shuffle Lie algebra
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916884987772928 |
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| author | Burmester, Annika |
| author_facet | Burmester, Annika |
| contents | The linearized double shuffle Lie algebra $\mathfrak{ls}$ is a well-studied Lie algebra, which reflects the depth-graded structure of multiple zeta values. We introduce a generalization $\mathfrak{lq}$, which is motivated from the $\mathbb{Q}$-algebraic structure of multiple q-zeta values and multiple Eisenstein series. Precisely, we show that $\mathfrak{lq}$ is a Lie algebra, where the Lie bracket is related to Ecalle's ari bracket on bimoulds, and give an embedding of $\mathfrak{ls}$ into $\mathfrak{lq}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05024 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An extension of the linearized double shuffle Lie algebra Burmester, Annika Number Theory Rings and Algebras 11M32, 17B62, 05A30 The linearized double shuffle Lie algebra $\mathfrak{ls}$ is a well-studied Lie algebra, which reflects the depth-graded structure of multiple zeta values. We introduce a generalization $\mathfrak{lq}$, which is motivated from the $\mathbb{Q}$-algebraic structure of multiple q-zeta values and multiple Eisenstein series. Precisely, we show that $\mathfrak{lq}$ is a Lie algebra, where the Lie bracket is related to Ecalle's ari bracket on bimoulds, and give an embedding of $\mathfrak{ls}$ into $\mathfrak{lq}$. |
| title | An extension of the linearized double shuffle Lie algebra |
| topic | Number Theory Rings and Algebras 11M32, 17B62, 05A30 |
| url | https://arxiv.org/abs/2508.05024 |