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Simple Lie Group
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Summary
A
Simple Lie Group
is a
Non-abelian Lie group
that is connected and has no
Nontrivial connected normal subgroups
, serving as the
Building Blocks
for more
Complex Lie groups
. These groups are fundamental in understanding
Continuous Symmetries
and occur frequently in the study of
Differential Geometry
and
Theoretical Physics
, particularly in the
Classification of elementary particles
and
Gauge Theories
.
Concepts
Lie Algebra
Root System
Cartan Subalgebra
Dynkin Diagram
Algebraic Group
Representation Theory
Compact Lie Group
Semisimple Lie Group
Symmetric Space
Weyl Group
Dynkin Diagrams
Exceptional Group
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