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algebra > abstract algebra > algebraic structure > associative algebra > Weyl algebra

algebra > differential algebra > Weyl algebra

mathematical physics > differential operator > Weyl algebra

mathematical analysis > functional analysis > operator > differential operator > Weyl algebra

mathematical analysis > functional analysis > operator algebra > Weyl algebra

... > abstract algebra > algebraic structure > ring theory > operator algebra > Weyl algebra

Preferred term

Weyl algebra

Definition(s)

In abstract algebra, the Weyl algebra is the ring of differential operators with polynomial coefficients (in one variable), namely expressions of the form

${\\displaystyle f_{m}(X)\\partial _{X}^{m}+f_{m-1}(X)\\partial _{X}^{m-1}+\\cdots +f_{1}(X)\\partial _{X}+f_{0}(X).}$

More precisely, let F be the underlying field, and let F[X] be the ring of polynomials in one variable, X, with coefficients in F. Then each f_i lies in F[X].
∂_X is the derivative with respect to X. The algebra is generated by X and ∂_X.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Weyl_algebra)

Broader concept(s)

In other languages

algèbre de Weyl

French

URI

http://data.loterre.fr/ark:/67375/PSR-XP5BM1D2-V

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