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Concept
Cartan Matrix
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Summary
A
Cartan Matrix
is a
Square Matrix
used in the
Theory of Lie algebras
and
Algebraic Groups
, providing a compact representation of the
Structure Constants
of a
Semisimple Lie Algebra
. It is instrumental in classifying
Simple Lie Algebras
and is intimately linked to
Root Systems
and
Dynkin Diagrams
, serving as a bridge between algebraic and
Geometric Properties
of
Lie Groups
.
Concepts
Lie Algebra
Semisimple Lie Algebra
Root System
Dynkin Diagram
Simple Lie Algebra
Weyl Group
Kac-Moody Algebra
Coxeter Group
Bilinear Form
Representation Theory
Dynkin Diagrams
Affine Dynkin Diagram
Affine Lie Algebra
Simple Roots
Simple Root
Relevant Degrees
Algebra 70%
Geometry 30%
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