Difference between revisions of "Template:Lie groups"

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imported>TakuyaMurata
(List of simple Lie groups has been merged)
 
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<includeonly>{{Sidebar with collapsible lists
+
{{Sidebar with collapsible lists
 
| name = Lie groups
 
| name = Lie groups
| class = plainlist
+
| title = <!-- the group theory is often about finite groups so a link to [[group theory]] isn’t too relevant
| pretitlestyle = font-size:8pt; <!--font-weight:none--> padding-bottom:0.3em
+
<span style="font-size: 8pt; font-weight: none">[[Group theory]] → '''Lie groups'''</span>-->[[Lie group]]s
| pretitle = [[Group theory]] {{arrow/core|size=20}} [[Lie groups]]
+
| imagestyle = padding-bottom:0.9em;
| title = [[Lie groups]]
+
| image = [[File:E8Petrie.svg|frameless|180px<!--no greater than 180px, please, for sake of smaller screens/windows-->]]
| imagestyle = display:block;margin:0.4em 0 0.9em
+
| caption =  
| image = [[File:E8Petrie.svg|frameless|180px|link=E8 (mathematics)]]
+
| expanded = {{{expanded|{{{1|}}}}}}
| listtitlestyle = text-align:center; border-bottom:1px solid #aaa
 
| liststyle = padding-left:0.35em; padding-right:0.35em; border-bottom:1px solid #aaa
 
| expanded = {{{cTopic|{{{expanded|{{{1|}}}}}}}}}
 
  
| list1name = classical
+
| content1 =  
| list1title = [[Classical group|Classical]]
 
| list1 =
 
* [[General linear group|General linear &nbsp;GL(''n'')]]
 
* [[Special linear group|Special linear &nbsp;SL(''n'')]]
 
* [[Orthogonal group|Orthogonal &nbsp;O(''n'')]]
 
* [[Special orthogonal group|Special orthogonal &nbsp;SO(''n'')]]
 
* [[Unitary group|Unitary &nbsp;U(''n'')]]
 
* [[Special unitary group|Special unitary &nbsp;SU(''n'')]]
 
* [[Symplectic group|Symplectic &nbsp;Sp(''n'')]]
 
  
| list3name = simple
+
<!-------------------- Classical -------------------------->
| list3title = [[Simple Lie group|Simple]]
+
 
| list3class = hlist
+
| list2name = Classical
| list3 =
+
| list2title = [[Classical group]]s
* [[List of simple Lie groups]]
+
| list2 = <div class="plainlist">
<div style="margin-top:0.25em;line-height:1.1em"> ''Classical''
+
* [[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'')
 +
</div>
 +
 
 +
 
 +
<!---------------------- 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#A series|A<sub>''n''</sub>]]
 
* [[Simple Lie group#B series|B<sub>''n''</sub>]]
 
* [[Simple Lie group#B series|B<sub>''n''</sub>]]
 
* [[Simple Lie group#C series|C<sub>''n''</sub>]]
 
* [[Simple Lie group#C series|C<sub>''n''</sub>]]
 
* [[Simple Lie group#D series|D<sub>''n''</sub>]]
 
* [[Simple Lie group#D series|D<sub>''n''</sub>]]
</div> <div style="margin-top:0.6em;line-height:1.1em"> ''Exceptional''
+
 
 +
|heading3 = Exceptional
 +
|content3 =
 
* [[G2 (mathematics)|G<sub>2</sub>]]
 
* [[G2 (mathematics)|G<sub>2</sub>]]
 
* [[F4 (mathematics)|F<sub>4</sub>]]
 
* [[F4 (mathematics)|F<sub>4</sub>]]
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* [[E7 (mathematics)|E<sub>7</sub>]]
 
* [[E7 (mathematics)|E<sub>7</sub>]]
 
* [[E8 (mathematics)|E<sub>8</sub>]]
 
* [[E8 (mathematics)|E<sub>8</sub>]]
</div>
+
}}
 +
 
 +
<!----------------------- Other --------------------------->
  
| list4name = other
+
| list4name = Other
| list4title = [[Table of Lie groups|Other]]
+
| list4title = [[Table of Lie groups|Other Lie groups]]
| list4class = hlist
+
| list4 = <div class="hlist">
| list4 =
 
 
* [[Circle group|Circle]]
 
* [[Circle group|Circle]]
 
* [[Lorentz group|Lorentz]]
 
* [[Lorentz group|Lorentz]]
 
* [[Poincaré group|Poincaré]]
 
* [[Poincaré group|Poincaré]]
* [[Conformal group|Conformal]]
+
* [[Conformal group]]
 
* [[Diffeomorphism]]
 
* [[Diffeomorphism]]
 
* [[Loop group|Loop]]
 
* [[Loop group|Loop]]
 +
* [[Euclidean group|Euclidean]]
 +
</div>
  
| list5name = algebras
+
 
| list5title = [[Lie algebra|Algebra]]s
+
<!--------------------- Algebras -------------------------->
| list5 = <div class="hlist" style="margin-bottom:0.4em">
+
 
* [[Simple Lie algebra|Simple]]
+
| list5name = Algebras
 +
| list5title = [[Lie algebra]]s
 +
| list5 = <div class="plainlist">
 +
* [[Lie group–Lie algebra correspondence]]
 
* [[Exponential map (Lie theory)|Exponential map]]
 
* [[Exponential map (Lie theory)|Exponential map]]
 
* [[Adjoint representation]]
 
* [[Adjoint representation]]
** [[Adjoint representation|group]]
+
* {{hlist |[[Killing form]] |[[Index of a Lie algebra|Index]]}}
** [[Adjoint endomorphism|algebra]]
 
* [[Killing form]]
 
* [[Index of a Lie algebra|Index]]
 
 
* [[Lie point symmetry]]
 
* [[Lie point symmetry]]
</div> ''[[Semisimple Lie algebra|Semisimple]]''
+
*[[Simple Lie algebra]]
<div class="hlist" style="margin-top:0.15em;border-top:1px solid #aaa">
+
</div>
 +
 
 +
 
 +
<!-------------------- Semi-simple ------------------------>
 +
 
 +
| list6name = Semi-simple
 +
| list6title = [[Semisimple Lie algebra]]
 +
| list6 = <div class="plainlist">
 
* [[Dynkin diagram]]s
 
* [[Dynkin diagram]]s
 
* [[Cartan subalgebra]]
 
* [[Cartan subalgebra]]
* [[Root system]]
+
* {{hlist |[[Root system]] |[[Weyl group]]}}
* [[Weyl group]]
+
* {{hlist |[[Real form (Lie theory)|Real form]] |[[Complexification (Lie group)|Complexification]]}}
* [[Real form (Lie theory)|Real form]]
 
* [[Complexification (Lie group)|Complexification]]
 
 
* [[Split Lie algebra]]
 
* [[Split Lie algebra]]
 
* [[Compact Lie algebra]]
 
* [[Compact Lie algebra]]
 
</div>
 
</div>
  
| list6name = homogeneous
 
| list6title = [[Homogeneous space]]s
 
| list6 =
 
* [[Borel–de Siebenthal theory|Closed subgroup]]
 
* [[Parabolic subgroup]]
 
* [[Symmetric space]]
 
* [[Hermitian symmetric space]]
 
* [[Restricted root system]]
 
  
| list7name = representation
+
<!------------------ Representation ----------------------->
| list7title = [[Representation theory]]
+
 
| list7class = hlist
+
| list8name = Representation
| list7 =
+
| list8title = [[Representation theory]]
* [[Representation of a Lie group|Lie group]]
+
| list8 = <div class="plainlist">
* [[Lie algebra representation|Lie algebra]]
+
* [[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]]
 +
</div>
 +
 
 +
 
 +
<!---------------------- Physics -------------------------->
  
| list8name = physics
+
| list9name = Physics
| list8title = Lie groups in [[physics]]
+
| list9title = Lie groups in [[physics]]
| list8 =
+
| list9 = <div class="plainlist">
* {{longitem|style=padding:0.3em 0 0.2em|[[Particle physics and representation theory]]}}
+
* [[Particle physics and representation theory]]
 
* [[Representation theory of the Lorentz group|Lorentz group representations]]
 
* [[Representation theory of the Lorentz group|Lorentz group representations]]
 
* [[Representation theory of the Poincaré group|Poincaré group representations]]
 
* [[Representation theory of the Poincaré group|Poincaré group representations]]
 
* [[Representation theory of the Galilean group|Galilean group representations]]
 
* [[Representation theory of the Galilean group|Galilean group representations]]
 +
</div>
 +
 +
 +
<!-------------------- Scientists ------------------------->
  
| list9name = people
+
| list10name = Scientists
| list9title = People
+
| list10title = Scientists
| list9class = hlist
+
| list10 = <div class="hlist">
| list9 =
+
*[[Sophus Lie]]
* [[Sophus Lie]]
+
*[[Henri Poincaré]]
* [[Henri Poincaré]]
+
*[[Wilhelm Killing]]
* [[Wilhelm Killing]]
+
*[[Élie Cartan]]
* [[Élie Cartan]]
+
*[[Hermann Weyl]]
* [[Hermann Weyl]]
+
*[[Claude Chevalley]]
* [[Claude Chevalley]]
+
*[[Harish-Chandra]]
* [[Harish-Chandra]]
+
*[[Armand Borel]]
* [[Armand Borel]]
+
</div>
  
| belowstyle = margin-top:0; border:none; padding-top:0
+
 
 +
| belowclass = plainlist
 
| below =
 
| below =
 +
* [[Glossary of Lie groups and Lie algebras|Glossary]]
 
* [[Table of Lie groups]]
 
* [[Table of Lie groups]]
  
}}</includeonly><noinclude>
+
}}<noinclude>
{{Documentation
+
 
| content = {{Lie groups}}
+
{{collapsible lists option
{{Collapsible lists option
+
|listnames = Classical, Simple, Other, Algebras, Semi-simple, Homegeneous space,<br/>Representation, Physics, Scientists
| listnames = {{hlist |classical |simple |other |algebras |homegeneous |representation |physics |people}}
+
|example = Homogeneous space
| example = semi-simple
 
 
}}
 
}}
  
 
[[Category:Mathematics sidebar templates]]
 
[[Category:Mathematics sidebar templates]]
 
[[Category:Physics sidebar templates]]
 
[[Category:Physics sidebar templates]]
}}</noinclude>
+
 
 +
</noinclude>

Latest revision as of 19:25, 20 January 2021

This template includes collapsible lists.

  • To set it to display all lists when it appears (i.e. all lists expanded), use:
  •  {{Lie groups |expanded=all}} or, if enabled, {{Lie groups |all}}  (i.e. omitting "expanded=").
  • To set it to display one particular list while keeping the remainder collapsed (i.e. hidden apart from their headings), use:
  •  {{Lie groups |expanded=listname}} or, if enabled, {{Lie groups |listname}}
  • …where listname is one of the following (do not include any quotemarks):
  • Classical, Simple, Other, Algebras, Semi-simple, Homegeneous space,
    Representation, Physics, Scientists
  • For example, {{Lie groups |expanded=Homogeneous space}} or, if enabled, {{Lie groups |Homogeneous space}}