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Witt Algebra

The Witt algebra over C is the Lie algebra of derivations of C[z,z^(-1)]. With basis L_n=-z^(n+1)d/dz for n in Z, its bracket is

[L_m,L_n]=(m-n)L_(m+n).

The Virasoro algebra adds a central term to this bracket and has the Witt algebra as its quotient by the central line. This derivation convention fixes the sign in the bracket used for conformal modes.

See also

Derivation, Lie Algebra, Virasoro Algebra

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References

Bump, D. "Lecture 2: Conformal Mappings." Jan. 1, 2020. https://sporadic.stanford.edu/conformal/lecture2.pdf.Keller, C. A. Introduction to Vertex Operator Algebras. Lecture Notes, Dec. 13, 2017. https://archive.math.arizona.edu/cakeller/VertexOperatorAlgebras.pdf.

Cite this as:

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

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