Uniqueness of the non-commutative divergence cocycle
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911410261327872 |
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| author | Baudat, Pauline |
| author_facet | Baudat, Pauline |
| contents | We show that, for $n \geq 3 $, 1-cocycles of degree zero on the Lie algebra of derivations of the free associative algebra $T(A_n)$ with values in $ \rvert T(A_n) \rvert \otimes \rvert T(A_n) \rvert $ are linear combinations of the non-commutative divergence and its switch, when restricted to finite-degree quotients. Here, $ \rvert T(A_n) \rvert $ denotes the space of cyclic words. Furthermore, we study 1-cocycles of degree zero on the Lie algebra of symplectic derivations of the free Lie algebra $ \mathfrak{L_{2n}}$, and prove the uniqueness of the Enomoto-Satoh trace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06903 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniqueness of the non-commutative divergence cocycle Baudat, Pauline Quantum Algebra We show that, for $n \geq 3 $, 1-cocycles of degree zero on the Lie algebra of derivations of the free associative algebra $T(A_n)$ with values in $ \rvert T(A_n) \rvert \otimes \rvert T(A_n) \rvert $ are linear combinations of the non-commutative divergence and its switch, when restricted to finite-degree quotients. Here, $ \rvert T(A_n) \rvert $ denotes the space of cyclic words. Furthermore, we study 1-cocycles of degree zero on the Lie algebra of symplectic derivations of the free Lie algebra $ \mathfrak{L_{2n}}$, and prove the uniqueness of the Enomoto-Satoh trace. |
| title | Uniqueness of the non-commutative divergence cocycle |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2511.06903 |