Difference between revisions of "Template:Lie groups"
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imported>Mathsci |
imported>TakuyaMurata (List of simple Lie groups has been merged) |
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{{Sidebar with collapsible lists | {{Sidebar with collapsible lists | ||
| name = Lie groups | | name = Lie groups | ||
| − | | style = | + | | 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'''</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--> | + | | image = [[File:E8Petrie.svg|frameless|180px<!--no greater than 180px, please, for sake of smaller screens/windows-->]] |
| caption = | | caption = | ||
| − | |||
| expanded = {{{expanded|{{{1|}}}}}} | | expanded = {{{expanded|{{{1|}}}}}} | ||
| content1 = | | content1 = | ||
| − | |||
<!-------------------- Classical --------------------------> | <!-------------------- Classical --------------------------> | ||
| Line 16: | Line 14: | ||
| 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) | ||
| Line 36: | Line 29: | ||
| list3name = Simple | | list3name = Simple | ||
| list3title = [[Simple Lie group]]s | | list3title = [[Simple Lie group]]s | ||
| − | | list3 = | + | | list3 = {{sidebar|navbar=off |
| − | + | | bodystyle = {{subsidebar bodystyle}} | |
| − | {{ | + | | bodyclass = hlist |
| − | + | | headingstyle = font-weight:normal; font-style:italic; | |
| − | + | ||
| − | * [[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>]] | |
| − | + | * [[Simple Lie group#D series|D<sub>''n''</sub>]] | |
| − | | | + | |
| − | | | + | |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>]] | ||
| Line 55: | Line 49: | ||
* [[E8 (mathematics)|E<sub>8</sub>]] | * [[E8 (mathematics)|E<sub>8</sub>]] | ||
}} | }} | ||
| − | |||
<!----------------------- Other ---------------------------> | <!----------------------- Other ---------------------------> | ||
| Line 61: | Line 54: | ||
| 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> | ||
| Line 76: | Line 69: | ||
| list5name = Algebras | | list5name = Algebras | ||
| list5title = [[Lie algebra]]s | | list5title = [[Lie algebra]]s | ||
| − | | list5 = | + | | list5 = <div class="plainlist"> |
| − | * [[ | + | * [[Lie group–Lie algebra correspondence]] |
| − | + | * [[Exponential map (Lie theory)|Exponential map]] | |
| − | * [[Killing form]] | + | * [[Adjoint representation]] |
| − | + | * {{hlist |[[Killing form]] |[[Index of a Lie algebra|Index]]}} | |
| − | |||
* [[Lie point symmetry]] | * [[Lie point symmetry]] | ||
| + | *[[Simple Lie algebra]] | ||
| + | </div> | ||
| Line 88: | Line 82: | ||
| list6name = Semi-simple | | list6name = Semi-simple | ||
| − | | list6title = [[Semisimple Lie algebra | + | | 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]]}} |
| − | |||
| − | |||
| − | * [[Real form (Lie theory)|Real form]] | ||
| − | |||
| − | |||
* [[Split Lie algebra]] | * [[Split Lie algebra]] | ||
| − | |||
* [[Compact Lie algebra]] | * [[Compact Lie algebra]] | ||
| + | </div> | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
<!------------------ Representation -----------------------> | <!------------------ Representation -----------------------> | ||
| Line 119: | Line 97: | ||
| 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> | ||
| Line 130: | Line 111: | ||
| 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 theory]] |
| − | + | * [[Representation theory of the Lorentz group|Lorentz group representations]] | |
| − | * [[Representation theory of the Lorentz group|Lorentz group | + | * [[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 | + | </div> |
| − | |||
| − | * [[Representation theory of the Galilean group|Galilean group | ||
| Line 144: | Line 123: | ||
| list10name = Scientists | | list10name = Scientists | ||
| list10title = Scientists | | list10title = Scientists | ||
| − | | list10 = < | + | | list10 = <div class="hlist"> |
| − | |||
*[[Sophus Lie]] | *[[Sophus Lie]] | ||
*[[Henri Poincaré]] | *[[Henri Poincaré]] | ||
| + | *[[Wilhelm Killing]] | ||
*[[Élie Cartan]] | *[[Élie Cartan]] | ||
*[[Hermann Weyl]] | *[[Hermann Weyl]] | ||
| Line 153: | Line 132: | ||
*[[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]] | ||
| Line 161: | Line 143: | ||
{{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]] | ||
| − | |||
| − | |||
</noinclude> | </noinclude> | ||
Latest revision as of 19:25, 20 January 2021
| Lie groups |
|---|
| 180px |
|
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}}