Weyl Algebra
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High Quality Content by WIKIPEDIA articles! In abstract algebra, the Weyl algebra is the ring of differential operators with polynomial coefficients (in one variable), f_n(X) partial_X^n + cdots + f_1(X) partial_X + f_0(X). More precisely, let F be a field, and let F(X) be the ring of polynomials in one variable, X, with coefficients in F. Then each fi lies in F(X). X is the derivative with respect to X. The algebra is generated by X and X. The Weyl algebra is an example of a simple ring that is not a matrix ring over a division ring. It is also a noncommutative example of a domain, and an exa...
High Quality Content by WIKIPEDIA articles! In abstract algebra, the Weyl algebra is the ring of differential operators with polynomial coefficients (in one variable), f_n(X) partial_X^n + cdots + f_1(X) partial_X + f_0(X). More precisely, let F be a field, and let F(X) be the ring of polynomials in one variable, X, with coefficients in F. Then each fi lies in F(X). X is the derivative with respect to X. The algebra is generated by X and X. The Weyl algebra is an example of a simple ring that is not a matrix ring over a division ring. It is also a noncommutative example of a domain, and an example of an Ore extension. The Weyl algebra is a quotient of the free algebra on two generators, X and Y, by the ideal generated by the single relation: YX - XY - 1.
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