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On a Pre-Lie Algebra Defined by Insertion of Rooted Trees
| Content Provider | Semantic Scholar |
|---|---|
| Author | Saïdi, Abdellatif |
| Copyright Year | 2010 |
| Abstract | Let K be a field of characteristic zero. For $${n \in \mathbb{N}^{*}}$$ , let $${\mathcal{T}^{\,\prime}_{n}}$$ be the vector space of non-planar rooted trees with n vertices (Foissy in Bull Sci Math 126, no. 3, 193–239; no. 4, 249–288, 2002). Let $${\vartriangleright}$$ be the left pre-Lie product of insertion of a tree inside another defined on infinitesimal characters of the graded Hopf algebra $${\mathcal{H}}$$ introduced by Calaque, Ebrahimi-Fard and Manchon. Let $${\mathcal{T}^{\,\prime}=\oplus_{n\geq 2}\mathcal{T}^{\,\prime}_{n}}$$ . In this work, we first prove that $${(\mathcal{T}^{\,\prime}, \vartriangleright)}$$ a pre-Lie algebra generated by the two ladders E1 and E2 where E1 is the ladder with one edge and E2 is the ladder with two edges. Second, we prove that $${(\mathcal{T}^{\,\prime}, \vartriangleright)}$$ is not a free pre-Lie algebra, and we exhibit a family of relations. |
| Starting Page | 181 |
| Ending Page | 196 |
| Page Count | 16 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s11005-010-0377-5 |
| Volume Number | 92 |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/s11005-010-0377-5 |
| Alternate Webpage(s) | https://doi.org/10.1007/s11005-010-0377-5 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
