Weyl algebra

noun

The ring of differential operators with polynomial coefficients (in one variable), namely expressions of the form f_m(X)∂_Xᵐ+f_m-1(X)∂_Xᵐ⁻¹+⋯+f_1(X)∂_X+f_0(X).

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Meanings

nounWeyl algebra (plural Weyl algebras)

plural Weyl algebras

  1. algebraThe ring of differential operators with polynomial coefficients (in one variable), namely expressions of the form f_m(X)∂_Xᵐ+f_m-1(X)∂_Xᵐ⁻¹+⋯+f_1(X)∂_X+f_0(X).

Origin

Named after Hermann Weyl, who introduced them to study the Heisenberg uncertainty principle in quantum mechanics.

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Cite this entry
APA

Weyl algebra. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Weyl%20algebra

MLA

“Weyl algebra.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Weyl%20algebra. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Weyl algebra,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Weyl%20algebra.

Source: Weyl algebra on Wiktionary, CC BY-SA 4.0.