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

  • A
  • Thread starter dx
  • Start date
  • #1
dx
Homework Helper
Gold Member
2,147
50
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 Lp 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 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.
 
Last edited:
Physics news on Phys.org
  • #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?
 
  • Like
Likes fresh_42
  • #3
I'd fear less the modular Lie algebras as I would fear the modular analysis!
 
  • #4
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.
 

Similar threads

Linear Functionals, Dual Spaces & Linear Transformations Between Them
    • Linear and Abstract Algebra
Replies
8
Views
4K
Explicit construction of isomorphisms of low-rank Lie algebras.
    • Linear and Abstract Algebra
Replies
2
Views
4K
Programs How good is this applied math program?
    • STEM Academic Advising
Replies
13
Views
2K
A Is the Counterfactual Argument for Locality and Realism Flawed?
    • Quantum Physics
Replies
11
Views
2K
What Are Hamel & Schauder Bases and How Do They Relate to Vector Spaces?
    • Linear and Abstract Algebra
Replies
13
Views
9K
Challenge Intermediate Math Challenge - June 2018
    • Math Proof Training and Practice
2
Replies
55
Views
8K
Quantum Reading list recommendation for HEP-ph to HEP-th/math-ph transition
    • Science and Math Textbooks
Replies
0
Views
635
Requesting suggestions for languages, libraries, and architectures for parallel (and sometimes non parallel) numerical and scientific computations
    • Programming and Computer Science
Replies
8
Views
1K
Challenge Intermediate Math Challenge - September 2018
    • Math Proof Training and Practice
Replies
28
Views
5K
Integral Curves by Right-Translation of Lie-Algebraic Elements
    • Calculus and Beyond Homework Help
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top