A What are Modular Lie Algebras and How Do They Apply to Function Spaces?

[dx]

TL;DR Summary

function spaces more general than Lp

I feel that it is possible to construct function spaces more general than those of the type L^p using the theory of modular Lie algebras. Such spaces have been considered long ago by Musielak. essentially, one considers functions

∫ _ℝ φ(λ|f(x)|) dx

where φ is a convex function u^p, which can sometimes be relaxed to functions such as φ(u) = e^u - 1.
I welcome comments from anyone who is informed about such issues.

 

[martinbn]

What is the role of the Lie algebras?

What is the structure of these spaces?

What is the motivation?

Why in this forum, why not the analysis forum?

Any reference?

 

[fresh_42]

I'd fear less the modular Lie algebras as I would fear the modular analysis!

 

[dx]

I am aware that not everyone knows what a modular Lie algebra is, so I offer the following brief explanation. modular lie algebras also occur in string theory under the name Witt algebra. for instance there is the following
Lemma. Let f be an endomorphism of a finite-dimensional vector space V such that tr(fⁿ) = 0 ∀ n ∈ ℕ. Then f is nilpotent.
one must consider the characteristic of the underlying base field F, where char (F) = p > 0

 

[martinbn]

I am aware that not everyone knows what a modular Lie algebra is, so I offer the following brief explanation. modular lie algebras also occur in string theory under the name Witt algebra. for instance there is the following
Lemma. Let f be an endomorphism of a finite-dimensional vector space V such that tr(fⁿ) = 0 ∀ n ∈ ℕ. Then f is nilpotent.
one must consider the characteristic of the underlying base field F, where char (F) = p > 0

This is not a definition and as written is unralated to Lie algebras!

A modular Lie algebra is a Lie algebra over a field of positive characteristic.

 

[martinbn]

I am aware that not everyone knows what a modular Lie algebra is, so I offer the following brief explanation. modular lie algebras also occur in string theory under the name Witt algebra.

Witt algebra is something else.