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- Weyl_algebra abstract "In abstract algebra, the Weyl algebra is the ring of differential operators with polynomial coefficients (in one variable),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 elements of the formThe Weyl algebra is the first in an infinite family of algebras, also known as Weyl algebras. The n-th Weyl algebra, An, is the ring of differential operators with polynomial coefficients in n variables. It is generated by Xi and .Weyl algebras are named after Hermann Weyl, who introduced them to study the Heisenberg uncertainty principle in quantum mechanics. It is a quotient of the universal enveloping algebra of the Heisenberg algebra, the Lie algebra of the Heisenberg group, by setting the element 1 ofthe Lie algebra equal to the unit 1 of the universal enveloping algebra.The Weyl algebra is also referred to as the symplectic Clifford algebra. Weyl algebras represent the same structure for symplectic bilinear forms that Clifford algebras represent for non-degenerate symmetric bilinear forms.".
- Weyl_algebra wikiPageExternalLink 0504224.
- Weyl_algebra wikiPageID "491095".
- Weyl_algebra wikiPageRevisionID "603598909".
- Weyl_algebra hasPhotoCollection Weyl_algebra.
- Weyl_algebra subject Category:Algebras.
- Weyl_algebra subject Category:Differential_operators.
- Weyl_algebra subject Category:Ring_theory.
- Weyl_algebra type Abstraction100002137.
- Weyl_algebra type Algebra106012726.
- Weyl_algebra type Algebras.
- Weyl_algebra type Cognition100023271.
- Weyl_algebra type Content105809192.
- Weyl_algebra type DifferentialOperators.
- Weyl_algebra type Discipline105996646.
- Weyl_algebra type Function113783816.
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- Weyl_algebra type MathematicalRelation113783581.
- Weyl_algebra type Mathematics106000644.
- Weyl_algebra type Operator113786413.
- Weyl_algebra type PsychologicalFeature100023100.
- Weyl_algebra type PureMathematics106003682.
- Weyl_algebra type Relation100031921.
- Weyl_algebra type Science105999797.
- Weyl_algebra comment "In abstract algebra, the Weyl algebra is the ring of differential operators with polynomial coefficients (in one variable),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.".
- Weyl_algebra label "Algebra di Weyl".
- Weyl_algebra label "Weyl algebra".
- Weyl_algebra label "Weyl-algebra".
- Weyl_algebra label "Álgebra de Weyl".
- Weyl_algebra label "ワイル代数".
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- Weyl_algebra wasDerivedFrom Weyl_algebra?oldid=603598909.
- Weyl_algebra isPrimaryTopicOf Weyl_algebra.