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

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

φ(λ|f(x)|) dx

where φ is a convex function up, which can sometimes be relaxed to functions such as φ(u) = eu - 1.
I welcome comments from anyone who is informed about such issues.
 
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  • #2
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?
 
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  • #3
I'd fear less the modular Lie algebras as I would fear the modular analysis!
 
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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
 
  • #5
dx said:
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.
 
  • #6
dx said:
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.
 
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