1
$\begingroup$

I am looking for a explicit relation for adjoint cohomology of infinite dimensional Lie algebras (specifically smooth vector fields on a manifold), is it possible to apply Hochschild-Serre spectral sequence for these algebras?

$\endgroup$
  • 1
    $\begingroup$ There is no assumption of finite dimensionality for the Hochschild-Serre spectral sequence. $\endgroup$ – abx Jan 14 '18 at 19:36
3
$\begingroup$

A very useful source to learn about cohomology of infinite-dimensional Lie algebras is the book by D.B.Fuks "Cohomology of Infinite-Dimensional Lie Algebras" (shocking, I know). This source discusses Lie algebras of vector fields on manifolds, and applies the Hochschild-Serre spectral sequence in several different contexts. I suspect that going through that would resolve some of your concerns, and maybe settle many more of potential future questions.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.