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Loop Algebra

The loop algebra Lg of a Lie algebra g is the Lie algebra of the corresponding loop group. Its elements are smooth maps from the unit circle to g, and its Lie bracket is defined pointwise by

[X,Y](lambda)=[X(lambda),Y(lambda)].

As for loop groups, other regularity classes and complex-analytic extensions are used in applications.

See also

Lie Algebra, Loop Group

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References

Pressley, A. and Segal, G. Loop Groups. Oxford, England: Clarendon Press, 1986.

Cite this as:

Weisstein, Eric W. "Loop Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LoopAlgebra.html

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