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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 23rd 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarting something -- not done yet <a href="https://ncatlab.org/nlab/revision/tensor+hierarchy/1">v1</a>, <a href="https://ncatlab.org/nlab/show/tensor+hierarchy">current</a>

   starting something – not done yet

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 23rd 2020
   • (edited May 23rd 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to this proposal for understanding tensor hierarchies as [[L-infinity algebra]]-refinenents of [[Leibniz algebras]]: * [[Sylvain Lavau]], [[Jim Stasheff]], _$L_\infty$-algebra extensions of Leibniz algebras_ ([arXiv:2003.07838](https://arxiv.org/abs/2003.07838)) <a href="https://ncatlab.org/nlab/revision/tensor+hierarchy/1">v1</a>, <a href="https://ncatlab.org/nlab/show/tensor+hierarchy">current</a>

   added pointer to this proposal for understanding tensor hierarchies as L-infinity algebra-refinenents of Leibniz algebras:

   • Sylvain Lavau, Jim Stasheff, $L_\infty$-algebra extensions of Leibniz algebras (arXiv:2003.07838)

   v1, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 24th 2020
   • (edited May 24th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have started to make a note ([here](https://ncatlab.org/nlab/show/super+Lie+algebra#SuperLieAlgebraInducedFromVectorSpace)) on the "universal super Lie algebra on a vector space" that Jakob Palmkvist highlights on [p. 8 of arXiv:1305.0018](https://arxiv.org/pdf/1305.0018.pdf#page=8) (and more readably on [p. 8-9 of arXiv:1907.05752](https://arxiv.org/pdf/1907.05752.pdf#page=8)), attributed there to an article from 1970 by I. L. Kantor (which I can't find). I have tried to write out a proof of the super-Jacobi identity [here](https://ncatlab.org/nlab/show/super+Lie+algebra#SuperJacobiForSuperLieAlgebraInducedFromVectorSpace), but after some tedious typersetting of the would-be induction step, I find that the the actual induction argument (over the three degrees of the three elements involved in the Jacobi identity) is tricky. Or maybe I am too tired now. And maybe there is a much simpler argument. (?) <a href="https://ncatlab.org/nlab/revision/diff/tensor+hierarchy/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/tensor+hierarchy/7">v7</a>, <a href="https://ncatlab.org/nlab/show/tensor+hierarchy">current</a>

   I have started to make a note (here) on the “universal super Lie algebra on a vector space” that Jakob Palmkvist highlights on p. 8 of arXiv:1305.0018 (and more readably on p. 8-9 of arXiv:1907.05752), attributed there to an article from 1970 by I. L. Kantor (which I can’t find).

   I have tried to write out a proof of the super-Jacobi identity here, but after some tedious typersetting of the would-be induction step, I find that the the actual induction argument (over the three degrees of the three elements involved in the Jacobi identity) is tricky. Or maybe I am too tired now. And maybe there is a much simpler argument. (?)

   diff, v7, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 17th 2022
   • (edited Jul 17th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded pointer to the proposal for understanding tensor hierarchies via [[higher gauge theory]] with [[adjusted Weil algebras]]: * [[Leron Borsten]], [[Hyungrok Kim]], [[Christian Saemann]]. *$E L_\infty$-algebras, Generalized Geometry, and Tensor Hierarchies* &lbrack;[arXiv:2106.00108](https://arxiv.org/abs/2106.00108)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/tensor+hierarchy/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/tensor+hierarchy/10">v10</a>, <a href="https://ncatlab.org/nlab/show/tensor+hierarchy">current</a>

   Added pointer to the proposal for understanding tensor hierarchies via higher gauge theory with adjusted Weil algebras:

   • Leron Borsten, Hyungrok Kim, Christian Saemann. $E L_\infty$-algebras, Generalized Geometry, and Tensor Hierarchies [arXiv:2106.00108]

   diff, v10, current