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(This is an elaboration on the comment of MG. I know I benefited a lot as an undergraduate from being shown this sort of argument once instead of having been told to check things in local coordinates, …

I think your question, the way it is stated, makes one want to classify unary and binary (depending how far you generalise the question as written) invariant differential operators on tensor fields. T …

The Whitehouse module referred to in one of the other answers is not necessary, since it is related to the cyclic operad Lie, that is to the representation of $S_{n+1}$ in $Lie(n)$. The decomposition …

No. A skew-symmetric bilinear map $V\times V\to V$ satisfies the Jacobi identity automatically if $\dim V=2$ since the Jacobi identity is skew-symmetric in its arguments. So if you take a generic skew …

These constructions certainly are very recognisable and meaningful in the algebraic context, that is if you think of algebraic differential forms on an affine algebraic variety. Namely, the correspond …

It is very unhelpful that you give the wrong title of the paper you are asking for. In reality, the paper appears to be Cauchy's problem for Bach's equations of general relativity. R. Schimming Banach …

Some ideas of references that come to my mind right away: Fuks, Cohomology of infinite-dimensional Lie algebras. - contains lots of things that are relevant to your question Gelfand and Kazhdan, Cer …

Superalgebras have been used in various questions of algebra in a very striking way. To give some instances: Kemer's proof of the fact that, over a field of zero characteristic, every system of ident …