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Verma module

Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics.

Basic properties, Definition of Verma modules & Homomorphisms of Verma modules

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Overview

Informal construction

The case of sl(2; C)

Definition of Verma modules

Basic properties

Homomorphisms of Verma modules

Jordan–Hölder series

Bernstein–Gelfand–Gelfand resolution

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Verma module

Nodes69
Edges68
Triples108
Avg. degree1.97
Density0.028986
Components1

How this topic connects Entity context

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Verma module

Top relations

related to References · 47
Verma module → Affine Type, Algebra, Alvany, Amsterdam, An Elementary Introduction, Applications, BGG, Birkhäuser, Brian, Bäuerle, Cambridge University Press, Carter, Creative Commons Attribution/Share-Alike License, De Kerf, Dixmier, EMS PressRoggenkamp, Encyclopedia, Enveloping Algebras, Finite, Graduate Texts
related to Informal construction · 12
Verma module → Cartan, For, It, Let, Lie, Now, Our, Specifically, The Verma, Thus, Verma, We
related to Multiplicities · 7
Verma module → Birkhoff, Each, Kostant, Poincaré, This, Verma, Witt
related to The structure of the Verma module · 7
Verma module → Actually, Birkhoff, Lie, Poincaré, Verma, Whichever, Witt
related to Definition of Verma modules · 6
Verma module → Cartan, For, Lie, There, Verma, We
related to As a quotient of the enveloping algebra · 5
Verma module → Phi, Since, The, Thus, Verma
related to Bernstein–Gelfand–Gelfand resolution · 4
Verma module → Let, Lie, Verma, We
related to Irreducible quotient module · 4
Verma module → As, If, The, Verma
related to The case of sl(2; C) · 4
Verma module → Cartan, Let, Then, Verma
related to Other properties · 3
Verma module → In, The Verma, Weyl

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Important terminology

displaystyle verma module lambda weight mathfrak highest modules algebra lie dominant representation integral quotient irreducible vector finite-dimensional exists representations homomorphism

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Verma moduleis aquotient of the universal enveloping algebra U0.90text
Verma modulerelated to As a quotient of the enveloping algebraThe0.60section
Verma modulerelated to As a quotient of the enveloping algebraVerma0.60section
Verma modulerelated to As a quotient of the enveloping algebraSince0.60section
Verma modulerelated to As a quotient of the enveloping algebraThus0.60section
Verma modulerelated to As a quotient of the enveloping algebraPhi0.60section
Verma modulerelated to Basic propertiesVerma0.60section
Verma modulerelated to Basic propertiesThis0.60section
Verma modulerelated to Bernstein–Gelfand–Gelfand resolutionLet0.60section
Verma modulerelated to Bernstein–Gelfand–Gelfand resolutionLie0.60section
Verma modulerelated to Bernstein–Gelfand–Gelfand resolutionWe0.60section
Verma modulerelated to Bernstein–Gelfand–Gelfand resolutionVerma0.60section

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