Graded Lie superalgebras from embedding tensors
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908845696090112 |
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| author | Lavau, Sylvain Palmkvist, Jakob |
| author_facet | Lavau, Sylvain Palmkvist, Jakob |
| contents | We show how various constructions of $\mathbb{Z}$-graded Lie superalgebras are related to each other. These Lie superalgebras have a Lie algebra $\mathfrak{g}$ as the subalgebra at degree 0, an odd $\mathfrak{g}$-module V as the subspace at degree 1, and an embedding tensor as an element at degree -1. This is a linear map from V to $\mathfrak{g}$ satisfying a quadratic constraint, which equips V with the structure of a Leibniz algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23113 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Graded Lie superalgebras from embedding tensors Lavau, Sylvain Palmkvist, Jakob Representation Theory High Energy Physics - Theory Mathematical Physics Rings and Algebras We show how various constructions of $\mathbb{Z}$-graded Lie superalgebras are related to each other. These Lie superalgebras have a Lie algebra $\mathfrak{g}$ as the subalgebra at degree 0, an odd $\mathfrak{g}$-module V as the subspace at degree 1, and an embedding tensor as an element at degree -1. This is a linear map from V to $\mathfrak{g}$ satisfying a quadratic constraint, which equips V with the structure of a Leibniz algebra. |
| title | Graded Lie superalgebras from embedding tensors |
| topic | Representation Theory High Energy Physics - Theory Mathematical Physics Rings and Algebras |
| url | https://arxiv.org/abs/2601.23113 |