The nilradical of a seaweed algebra
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914329370034176 |
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| author | Coll, Vincent E. Mayers, Nicholas |
| author_facet | Coll, Vincent E. Mayers, Nicholas |
| contents | Seaweed subalgebras of $\mathfrak{gl}(n,\mathbb{C})$ and $\mathfrak{sl}(n,\mathbb{C})$ are combinatorially defined matrix Lie algebras whose index admits a closed-form description in terms of an associated graph called a meander. In this paper, we study the nilradicals of these algebras with our main result establishing an explicit formula for their index in terms of an edge-weighted variation of the meander. We further prove that each such nilradical decomposes as a direct sum of the center of the seaweed subalgebra with a nilpotent Lie poset algebra, and we provide a meander-theoretic procedure for recovering the underlying poset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13467 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The nilradical of a seaweed algebra Coll, Vincent E. Mayers, Nicholas Combinatorics Seaweed subalgebras of $\mathfrak{gl}(n,\mathbb{C})$ and $\mathfrak{sl}(n,\mathbb{C})$ are combinatorially defined matrix Lie algebras whose index admits a closed-form description in terms of an associated graph called a meander. In this paper, we study the nilradicals of these algebras with our main result establishing an explicit formula for their index in terms of an edge-weighted variation of the meander. We further prove that each such nilradical decomposes as a direct sum of the center of the seaweed subalgebra with a nilpotent Lie poset algebra, and we provide a meander-theoretic procedure for recovering the underlying poset. |
| title | The nilradical of a seaweed algebra |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.13467 |