Difference between revisions of "Template:Lie groups"

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imported>Mathsci
imported>TakuyaMurata
(List of simple Lie groups has been merged)
 
(38 intermediate revisions by 19 users not shown)
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{{Sidebar with collapsible lists
 
{{Sidebar with collapsible lists
 
| name = Lie groups
 
| name = Lie groups
| style = width:18.0em;
+
| title = <!-- the group theory is often about finite groups so a link to [[group theory]] isn’t too relevant
| title = [[Lie group]]s
+
<span style="font-size: 8pt; font-weight: none">[[Group theory]] → '''Lie groups'''</span>-->[[Lie group]]s
 
| imagestyle = padding-bottom:0.9em;
 
| imagestyle = padding-bottom:0.9em;
| image = [[File:E8Petrie.svg|frameless|180px<!--no greater than 180px, please, for sake of smaller screens/windows-->|link=E8 (mathematics)]]
+
| image = [[File:E8Petrie.svg|frameless|180px<!--no greater than 180px, please, for sake of smaller screens/windows-->]]
 
| caption =  
 
| caption =  
| listclass = hlist
 
 
| expanded = {{{expanded|{{{1|}}}}}}
 
| expanded = {{{expanded|{{{1|}}}}}}
  
 
| content1 =  
 
| content1 =  
 
  
 
<!-------------------- Classical -------------------------->
 
<!-------------------- Classical -------------------------->
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| list2name = Classical
 
| list2name = Classical
 
| list2title = [[Classical group]]s
 
| list2title = [[Classical group]]s
| list2 =
+
| list2 = <div class="plainlist">
* [[General linear group|General linear]] GL(n)
+
* [[General linear group|General linear]] GL(''n'')
 
+
* [[Special linear group|Special linear]] SL(''n'')
* [[Special linear group|Special linear]] SL(n)
+
* [[Orthogonal group|Orthogonal]] O(''n'')
 
+
* [[Special orthogonal group|Special orthogonal]] SO(''n'')
* [[Orthogonal group|Orthogonal]] O(n)
+
* [[Unitary group|Unitary]] U(''n'')
 
+
* [[Special unitary group|Special unitary]] SU(''n'')
* [[Special orthogonal group|Special orthogonal]] SO(n)
+
* [[Symplectic group|Symplectic]] Sp(''n'')
 
+
</div>
* [[Unitary group|Unitary]] U(n)
 
 
 
* [[Special unitary group|Special unitary]] SU(n)
 
 
 
* [[Symplectic group|Symplectic]] Sp(n)
 
  
  
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| list3name = Simple
 
| list3name = Simple
 
| list3title = [[Simple Lie group]]s
 
| list3title = [[Simple Lie group]]s
| list3 =
+
| list3 = {{sidebar|navbar=off
* [[List of simple Lie groups]]
+
| bodystyle = {{subsidebar bodystyle}}
{{Sidebar subsection |headingstyle=padding-top:0.2em;
+
| bodyclass = hlist
|heading = Classical
+
| headingstyle = font-weight:normal; font-style:italic;
|content =
+
 
* [[Simple Lie group#A series|A<sub>n</sub>]]
+
  |heading2 = Classical
* [[Simple Lie group#B series|B<sub>n</sub>]]
+
  |content2 =
* [[Simple Lie group#C series|C<sub>n</sub>]]
+
* [[Simple Lie group#A series|A<sub>''n''</sub>]]
* [[Simple Lie group#D series|D<sub>n</sub>]]
+
* [[Simple Lie group#B series|B<sub>''n''</sub>]]
}}
+
* [[Simple Lie group#C series|C<sub>''n''</sub>]]
{{Sidebar subsection
+
* [[Simple Lie group#D series|D<sub>''n''</sub>]]
  |heading = Exceptional
+
 
  |content =
+
  |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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* [[E8 (mathematics)|E<sub>8</sub>]]
 
* [[E8 (mathematics)|E<sub>8</sub>]]
 
}}
 
}}
 
  
 
<!----------------------- Other --------------------------->
 
<!----------------------- Other --------------------------->
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| list4name = Other
 
| list4name = Other
 
| list4title = [[Table of Lie groups|Other Lie groups]]
 
| list4title = [[Table of Lie groups|Other Lie groups]]
| list4 =
+
| list4 = <div class="hlist">
 
* [[Circle group|Circle]]
 
* [[Circle group|Circle]]
 
* [[Lorentz group|Lorentz]]
 
* [[Lorentz group|Lorentz]]
 
 
* [[Poincaré group|Poincaré]]
 
* [[Poincaré group|Poincaré]]
 
* [[Conformal group]]
 
* [[Conformal group]]
 
 
* [[Diffeomorphism]]
 
* [[Diffeomorphism]]
 
* [[Loop group|Loop]]
 
* [[Loop group|Loop]]
 +
* [[Euclidean group|Euclidean]]
 +
</div>
  
  
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| list5name = Algebras
 
| list5name = Algebras
 
| list5title = [[Lie algebra]]s
 
| list5title = [[Lie algebra]]s
| list5 =
+
| list5 = <div class="plainlist">
* [[Exponential map]]
+
* [[Lie group–Lie algebra correspondence]]
{{longlink |[[Adjoint representation]] {{hlist|([[Adjoint representation|group]]|[[Adjoint endomorphism|algebra]])}}}}
+
* [[Exponential map (Lie theory)|Exponential map]]
* [[Killing form]]
+
* [[Adjoint representation]]
* [[Index of a Lie algebra|Index]]
+
* {{hlist |[[Killing form]] |[[Index of a Lie algebra|Index]]}}
 
 
 
* [[Lie point symmetry]]
 
* [[Lie point symmetry]]
 +
*[[Simple Lie algebra]]
 +
</div>
  
  
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| list6name = Semi-simple
 
| list6name = Semi-simple
| list6title = [[Semisimple Lie algebra|Semi-simple Lie groups]]
+
| list6title = [[Semisimple Lie algebra]]
| list6 =
+
| list6 = <div class="plainlist">
 
* [[Dynkin diagram]]s
 
* [[Dynkin diagram]]s
 
 
* [[Cartan subalgebra]]
 
* [[Cartan subalgebra]]
 
+
* {{hlist |[[Root system]] |[[Weyl group]]}}
* [[Root system]]
+
* {{hlist |[[Real form (Lie theory)|Real form]] |[[Complexification (Lie group)|Complexification]]}}
* [[Weyl group]]
 
 
 
* [[Real form (Lie theory)|Real form]]
 
* [[Complexification (Lie group)|Complexification]]
 
 
 
 
* [[Split Lie algebra]]
 
* [[Split Lie algebra]]
 
 
* [[Compact Lie algebra]]
 
* [[Compact Lie algebra]]
 +
</div>
  
<!-------------------- Homogeneous spaces ------------------------>
 
 
| list7name = Homogeneous spaces
 
| list7title = [[Homogeneous space]]s
 
| list7 =
 
 
* [[Borel–de Siebenthal theory|Closed subgroup]]
 
* [[Parabolic subgroup]]
 
* [[Symmetric space]]
 
* [[Hermitian symmetric space]]
 
  
 
<!------------------ Representation ----------------------->
 
<!------------------ Representation ----------------------->
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| list8name = Representation
 
| list8name = Representation
 
| list8title = [[Representation theory]]
 
| list8title = [[Representation theory]]
| list8 =
+
| list8 = <div class="plainlist">
 
* [[Representation of a Lie group|Lie group representation]]
 
* [[Representation of a Lie group|Lie group representation]]
 
 
* [[Lie algebra 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>
  
  
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| list9name = Physics
 
| list9name = Physics
 
| list9title = Lie groups in [[physics]]
 
| list9title = Lie groups in [[physics]]
| list9 =
+
| list9 = <div class="plainlist">
* [[Particle physics and representation theory|Particle physics and representation]]
+
* [[Particle physics and representation theory]]
 
+
* [[Representation theory of the Lorentz group|Lorentz group representations]]
* [[Representation theory of the Lorentz group|Lorentz group representation]]
+
* [[Representation theory of the Poincaré group|Poincaré group representations]]
 
+
* [[Representation theory of the Galilean group|Galilean group representations]]
* [[Representation theory of the Poincaré group|Poincaré group representation]]
+
</div>
 
 
* [[Representation theory of the Galilean group|Galilean group representation]]
 
  
  
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| list10name = Scientists
 
| list10name = Scientists
 
| list10title = Scientists
 
| list10title = Scientists
| list10 = <!--[[Contributors to ...|''others'']]-->
+
| list10 = <div class="hlist">
 
 
 
*[[Sophus Lie]]
 
*[[Sophus Lie]]
 
*[[Henri Poincaré]]
 
*[[Henri Poincaré]]
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*[[Harish-Chandra]]
 
*[[Harish-Chandra]]
 
*[[Armand Borel]]
 
*[[Armand Borel]]
 +
</div>
 +
  
 
| belowclass = plainlist
 
| belowclass = plainlist
 
| below =
 
| below =
 +
* [[Glossary of Lie groups and Lie algebras|Glossary]]
 
* [[Table of Lie groups]]
 
* [[Table of Lie groups]]
  
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{{collapsible lists option
 
{{collapsible lists option
  |listnames = Classical, Simple, Other, Algebras, Semi-simple, Homegeneous space, Representation, Physics, Scientists
+
  |listnames = Classical, Simple, Other, Algebras, Semi-simple, Homegeneous space,<br/>Representation, Physics, Scientists
 +
|example = Homogeneous space
 
}}
 
}}
  
[[Category:Mathematics templates]]
+
[[Category:Mathematics sidebar templates]]
 
[[Category:Physics sidebar templates]]
 
[[Category:Physics sidebar templates]]
[[Category:Physics templates]]
 
  
[[zh:Template:李群]]
 
 
</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}}