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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
added a few references and links to super Lie algebra
I have expanded the Definition-section at super Lie algebra, stating more variants of equivalent definitions. This is material taken from the more comprehensive lecture notes at geometry of physics – superalgebra.
added some minimum cross-link with Whitehead product
added doi for:
I have added some discussion (here) of the super Lie algebra of multilinear maps $V^{\otimes_n} \to V$ for any finite-dimensional vector space $V$, following Palmkvist 13, 3.1, Lavau-Palmkvist 19, 2.4 (my proof of the super-Jacobi identity remains incomplete, despite the lengthy computation).
The discussion culminates in the observation that “embedding tensors” are equivalently elements of square=0 and degree = -1 in this algebra, and hence are equivalently the datum to turn it into a dg-Lie algebra – supposedly (up to some restrictions and extensions) the “tensor hierarchy” induced by the embedding tensor. Which is a neat observation.
This super Lie algebra ought to have some standard name? Palmkvist attributes it to
but I haven’t found an actual copy of this article yet.
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