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ag.algebraic geometry – Lie bracket on the unshifted tangent complicated?
My drawback is as follows: if X is a derived strategy, or derived stack, or any kindly of an area the place tangent complicated is smart, I speculate there ought to breathe a equivocate bracket on its tangent complicated, extending the understanding of commutator of vector fields in flush underived areas. However, I’m unable to seek out something written on this path.
What I think about (principally following answeres to an identical query What is the relation between the Lie bracket on TX as commutator and that coming from the Atiyah class?) is that one can cerebrate of the tangent complicated as “representing” the formal completion of the diagonal of the product groupoid XxX and therefore have a construction of equivocate algebroid, or alternatively, that there ought to breathe (roughly talking) some kindly of a bracket that’s Koszul twin to the deRhan differential, however I am unable to discover any of this written down. Maybe it’s simply that my googling expertise failed me. I might value any ameliorate.
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