Lie Algebras and Homotopy Theory - Jacob Lurie
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users cite it as a source when asking about specific definitions and claims Lurie makes, such as Lie algebras over Z-modules, the commutator map, and a category of functors.
Recommended by 0 people across 0 different months, 2019 to 2021.
What it is
A one-hour Members' Seminar at the Institute for Advanced Study in which Jacob Lurie discusses Lie algebras from the viewpoint of homotopy theory. It covers how Lie algebras can be defined over abelian groups alone, and ends with a category of functors tied to universal Lie algebras.
What people said
Cites Bizfold · 2019-11 · Mathematics Stack Exchange · on “Abstract definition of a vector space”
Thank you very much. This is very helpful! The question was triggered while watching Jacob Lurie‘s lecture [this video] where he defines a Lie algebra on the basis of an abelian group only. No mentioning of a field or even a ring. So just on a Z module...
Cites theduckgoesquark · 2020-04 · Mathematics Stack Exchange · on “Relation between commutator map of Lie Group and Lie Algebra”
In the following video [this video] , 5 minutes in, he says that the differential of the commutator map gives the tangent space a Lie algebra structure. However, the answer here [LINK] clearly proves that the map is the zero map. What does he exactly mean in the video?
Cites Math.mx · 2021-10 · Mathematics Stack Exchange · on “Reference for the category of functors from finite sets with surjections to abelian groups”
In the talk of Jacob Lurie about Lie Algebras and Homotopy theory, he mention at the end about a category of functors that has the same derived category as the category as some category of universal Lie algebras. I found a reference of the universal Lie Algebra, in the paper "The universal Lie algebra" of P. Vogel, but I cannot find a reference of this category of functors. [this video]