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D-module

In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of linear partial differential equations. Since around 1970, D-module theory has been built up, mainly as a response to the ideas of Mikio Sato on algebraic analysis, and expanding on the work of Sato and…

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Overview

Modules over the Weyl algebra

D-modules on algebraic varieties

Holonomic modules

Applications

Bibliography

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D-module

Nodes107
Edges106
Triples133
Avg. degree1.98
Density0.018692
Components1

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D-module

Top relations

related to Bibliography · 50
D-module → Academic Press, Académie, Algebraic D-Modules, Amsterdam, Armand, Beilinson, Bernstein, BF01389272, Bibcode, Birkhäuser Boston, Boston, Cambridge University Press, Comptes Rendus, D-modules, Doorn, EMS PressHotta, Encyclopedia, Inventiones Mathematicae, ISBN, ISSN
related to Holonomic modules over the Weyl algebra · 20
D-module → An, Artin, Bernstein, D-modules, DX, Finitely, FpAn, Hilbert, In, It, K-linear, More, Moreover, Noetherian, Notably, Rees, The, The Hilbert, These, Weyl
related to External links · 11
D-module → Algebraic, Algebraic Theory, Bernstein, D-modules, Dennis, Dragan, Gaitsgory, Geometric Representation Theory, Joseph, Lectures, PDF
related to D-modules on algebraic varieties · 8
D-module → D-modules, DX, DX-module, Giving, K-linear, OX-algebra, OX-module, The
related to Geometric representation theory · 7
D-module → Beilinson, Bernstein, D-modules, G/B, It, Langlands, Lie
related to Functoriality · 6
D-module → D-modules, DX, DY, For, The, This
related to General definition · 6
D-module → As, D-modules, DX, The, The Bernstein, Weyl
related to Modules over the Weyl algebra · 5
D-module → An, D-modules, It, The, Weyl
related to Properties and characterizations · 5
D-module → Also, For, Holonomic, K-vector, Li
has application · 4
D-module → Bernstein, D-modules, One, Sato

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Important terminology

d-modules differential holonomic algebraic theory dx algebra ring left bernstein module polynomial bundle modules weyl hilbert defined right operators characteristic

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
D-moduleis amodule over a ring D of differential operators0.90text
Hilbert polynomialinstance ofstandard notions from commutative algebra0.80text
multiplicityinstance ofstandard notions from commutative algebra0.80text
length of modules carry over to D-modulesinstance ofstandard notions from commutative algebra0.80text
D-modulehas applicationOne0.60section
D-modulehas applicationD-modules0.60section
D-modulehas applicationBernstein0.60section
D-modulehas applicationSato0.60section
D-modulerelated to BibliographyLock-green0.60section
D-modulerelated to BibliographyLock-gray-alt-20.60section
D-modulerelated to BibliographyLock-red-alt-20.60section
D-modulerelated to BibliographyWikisource-logo0.60section

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