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{{Sidebar with collapsible lists
| name = Lie groups
| title = <!-- the group theory is often about finite groups so a link to [[group theory]] isn’t too relevant
<span style="font-size: 8pt; font-weight: none">[[Group theory]] → '''Lie groups and Lie algebras'''</span>-->[[Lie group]]s and [[Lie algebra]]s
| imagestyle = padding-bottom:0.9em;
| image = [[File:E8Petrie.svg|frameless|180px<!--no greater than 180px, please, for sake of smaller screens/windows-->]]
| caption = 
| expanded = {{{expanded|{{{1|}}}}}}

| content1 = 

<!-------------------- Classical -------------------------->

| list2name = Classical
| list2title = [[Classical group]]s
| list2 = {{plainlist|
* [[General linear group|General linear]] GL(''n'')
* [[Special linear group|Special linear]] SL(''n'')
* [[Orthogonal group|Orthogonal]] O(''n'')
* [[Special orthogonal group|Special orthogonal]] SO(''n'')
* [[Unitary group|Unitary]] U(''n'')
* [[Special unitary group|Special unitary]] SU(''n'')
* [[Symplectic group|Symplectic]] Sp(''n'')
}}


<!---------------------- Simple --------------------------->

| list3name = Simple
| list3title = [[Simple Lie group]]s
| list3 = {{sidebar|navbar=off
 | bodystyle = {{subsidebar bodystyle}}
 | bodyclass = hlist
 | headingstyle = font-weight:normal; font-style:italic;

  |heading2 = Classical
  |content2 =
* [[Simple Lie group#A series|A<sub>''n''</sub>]]
* [[Simple Lie group#B series|B<sub>''n''</sub>]]
* [[Simple Lie group#C series|C<sub>''n''</sub>]]
* [[Simple Lie group#D series|D<sub>''n''</sub>]]

 |heading3 = Exceptional
 |content3 =
* [[G2 (mathematics)|G<sub>2</sub>]]
* [[F4 (mathematics)|F<sub>4</sub>]]
* [[E6 (mathematics)|E<sub>6</sub>]]
* [[E7 (mathematics)|E<sub>7</sub>]]
* [[E8 (mathematics)|E<sub>8</sub>]]
}}

<!----------------------- Other --------------------------->

| list4name = Other
| list4title = [[Table of Lie groups|Other Lie groups]]
| list4 = {{flatlist|
* [[Circle group|Circle]]
* [[Lorentz group|Lorentz]]
* [[Poincaré group|Poincaré]]
* [[Conformal group]]
* [[Diffeomorphism]]
* [[Loop group|Loop]]
* [[Euclidean group|Euclidean]]
}}


<!--------------------- Algebras -------------------------->

| list5name = Algebras
| list5title = [[Lie algebra]]s
| list5 = {{plainlist|
* [[Lie group–Lie algebra correspondence]]
* [[Exponential map (Lie theory)|Exponential map]]
* [[Adjoint representation]]
* {{hlist |[[Killing form]] |[[Index of a Lie algebra|Index]]}}
* [[Simple Lie algebra]]
* [[Loop algebra]]
* [[Affine Lie algebra]]
}}


<!-------------------- Semi-simple ------------------------>

| list6name = Semi-simple
| list6title = [[Semisimple Lie algebra]]
| list6 = {{plainlist|
* [[Dynkin diagram]]s
* [[Cartan subalgebra]]
* {{hlist |[[Root system]] |[[Weyl group]]}}
* {{hlist |[[Real form (Lie theory)|Real form]] |[[Complexification (Lie group)|Complexification]]}}
* [[Split Lie algebra]]
* [[Compact Lie algebra]]
}}


<!------------------ Representation ----------------------->

| list8name = Representation
| list8title = [[Representation theory]]
| list8 = {{plainlist|
* [[Representation of a Lie group|Lie group representation]]
* [[Lie algebra representation]]
* [[Representation theory of semisimple Lie algebras]]
* [[Representations of classical Lie groups]]
* [[Theorem of the highest weight]]
* [[Borel–Weil–Bott theorem]]
}}


<!---------------------- Physics -------------------------->

| list9name = Physics
| list9title = Lie groups in [[physics]]
| list9 = {{plainlist|
* [[Particle physics and representation theory]]
* [[Representation theory of the Lorentz group|Lorentz group representations]]
* [[Representation theory of the Poincaré group|Poincaré group representations]]
* [[Representation theory of the Galilean group|Galilean group representations]]
}}


<!-------------------- Scientists ------------------------->

| list10name = Scientists
| list10title = Scientists
| list10 = {{flatlist|
*[[Sophus Lie]]
*[[Henri Poincaré]]
*[[Wilhelm Killing]]
*[[Élie Cartan]]
*[[Hermann Weyl]]
*[[Claude Chevalley]]
*[[Harish-Chandra]]
*[[Armand Borel]]
}}


| belowclass = plainlist
| below =
* [[Glossary of Lie groups and Lie algebras|Glossary]]
* [[Table of Lie groups]]

}}<noinclude>

{{collapsible lists option
 |listnames = Classical, Simple, Other, Algebras, Semi-simple, Homogeneous space,<br/>Representation, Physics, Scientists
 |example = Homogeneous space
}}

[[Category:Mathematics sidebar templates]]
[[Category:Physics sidebar templates]]

</noinclude>

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