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Kac-Moody Algebra
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Summary
Kac-Moody algebras
are an extension of
Finite-dimensional Lie algebras
, characterized by generators and relations encoded in a
Generalized Cartan matrix
, allowing for
Infinite-dimensional representations
. They play a crucial role in
Theoretical Physics
, particularly in
String Theory
and
Conformal Field Theory
, due to their
Rich structure
and
Symmetry properties
.
Concepts
Lie Algebras
Cartan Matrix
Root System
Affine Kac-Moody Algebra
Infinite-dimensional Representation
Weyl Group
Dynkin Diagram
Simple Roots
Conformal Field Theory
String Theory
Dynkin Diagrams
Affine Dynkin Diagram
Affine Lie Algebra
Loop Algebra
Affine Coxeter Group
Tits Cone
Boundary Conformal Field Theory
Relevant Degrees
Algebra 70%
Geometry 20%
Mathematical Analysis 10%
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