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arXiv · 2601.23113

Graded Lie superalgebras from embedding tensors

Sylvain Lavau·Jakob Palmkvist
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Abstract

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.

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Sylvain Lavau, Jakob Palmkvist. 2026-01-30. Graded Lie superalgebras from embedding tensors. https://arxiv.org/abs/2601.23113

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