Difference between revisions of "Template:Lie groups"
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imported>Mathsci |
imported>CsDix (class <div>s, collapsible lists option example) |
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| 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-->|link=E8 (mathematics)]] | ||
| caption = | | caption = | ||
| − | |||
| expanded = {{{expanded|{{{1|}}}}}} | | expanded = {{{expanded|{{{1|}}}}}} | ||
| Line 16: | Line 15: | ||
| 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) | * [[Orthogonal group|Orthogonal]] O(n) | ||
| − | |||
* [[Special orthogonal group|Special orthogonal]] SO(n) | * [[Special orthogonal group|Special orthogonal]] SO(n) | ||
| − | |||
* [[Unitary group|Unitary]] U(n) | * [[Unitary group|Unitary]] U(n) | ||
| − | |||
* [[Special unitary group|Special unitary]] SU(n) | * [[Special unitary group|Special unitary]] SU(n) | ||
| − | |||
* [[Symplectic group|Symplectic]] Sp(n) | * [[Symplectic group|Symplectic]] Sp(n) | ||
| + | </div> | ||
| Line 36: | Line 30: | ||
| list3name = Simple | | list3name = Simple | ||
| list3title = [[Simple Lie group]]s | | list3title = [[Simple Lie group]]s | ||
| − | | list3 = | + | | list3 = <div class="hlist"> |
* [[List of simple Lie groups]] | * [[List of simple Lie groups]] | ||
{{Sidebar subsection |headingstyle=padding-top:0.2em; | {{Sidebar subsection |headingstyle=padding-top:0.2em; | ||
| Line 55: | Line 49: | ||
* [[E8 (mathematics)|E<sub>8</sub>]] | * [[E8 (mathematics)|E<sub>8</sub>]] | ||
}} | }} | ||
| + | </div> | ||
| Line 61: | Line 56: | ||
| 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]] | ||
| + | </div> | ||
| Line 76: | Line 70: | ||
| list5name = Algebras | | list5name = Algebras | ||
| list5title = [[Lie algebra]]s | | list5title = [[Lie algebra]]s | ||
| − | | list5 = | + | | list5 = <div class="plainlist"> |
* [[Exponential map]] | * [[Exponential map]] | ||
| − | {{longlink |[[Adjoint representation]] {{hlist|([[Adjoint representation|group]]|[[Adjoint endomorphism|algebra]])}}}} | + | * {{longlink |[[Adjoint representation]] {{hlist|([[Adjoint representation|group]]|[[Adjoint endomorphism|algebra]])}}}} |
| − | * [[Killing form]] | + | * {{hlist |[[Killing form]] |[[Index of a Lie algebra|Index]]}} |
| − | |||
| − | |||
* [[Lie point symmetry]] | * [[Lie point symmetry]] | ||
| + | </div> | ||
| Line 89: | Line 82: | ||
| list6name = Semi-simple | | list6name = Semi-simple | ||
| list6title = [[Semisimple Lie algebra|Semi-simple Lie groups]] | | list6title = [[Semisimple Lie algebra|Semi-simple Lie groups]] | ||
| − | | 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]] | ||
| + | </div> | ||
| − | |||
<!-------------------- Homogeneous spaces ------------------------> | <!-------------------- Homogeneous spaces ------------------------> | ||
| Line 108: | Line 96: | ||
| list7name = Homogeneous spaces | | list7name = Homogeneous spaces | ||
| list7title = [[Homogeneous space]]s | | list7title = [[Homogeneous space]]s | ||
| − | | list7 = | + | | list7 = <div class="plainlist"> |
| − | |||
* [[Borel–de Siebenthal theory|Closed subgroup]] | * [[Borel–de Siebenthal theory|Closed subgroup]] | ||
* [[Parabolic subgroup]] | * [[Parabolic subgroup]] | ||
* [[Symmetric space]] | * [[Symmetric space]] | ||
* [[Hermitian symmetric space]] | * [[Hermitian symmetric space]] | ||
| + | </div> | ||
| + | |||
<!------------------ Representation -----------------------> | <!------------------ Representation -----------------------> | ||
| Line 119: | Line 108: | ||
| 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]] | ||
| − | + | </div> | |
| Line 130: | Line 118: | ||
| 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|Particle physics and representation]] | ||
| − | |||
* [[Representation theory of the Lorentz group|Lorentz group representation]] | * [[Representation theory of the Lorentz group|Lorentz group representation]] | ||
| − | |||
* [[Representation theory of the Poincaré group|Poincaré group representation]] | * [[Representation theory of the Poincaré group|Poincaré group representation]] | ||
| − | |||
* [[Representation theory of the Galilean group|Galilean group representation]] | * [[Representation theory of the Galilean group|Galilean group representation]] | ||
| + | </div> | ||
| Line 144: | Line 130: | ||
| list10name = Scientists | | list10name = Scientists | ||
| list10title = Scientists | | list10title = Scientists | ||
| − | | list10 = < | + | | list10 = <div class="hlist"> |
| − | |||
*[[Sophus Lie]] | *[[Sophus Lie]] | ||
*[[Henri Poincaré]] | *[[Henri Poincaré]] | ||
| Line 154: | Line 139: | ||
*[[Harish-Chandra]] | *[[Harish-Chandra]] | ||
*[[Armand Borel]] | *[[Armand Borel]] | ||
| + | </div> | ||
| + | |||
| belowclass = plainlist | | belowclass = plainlist | ||
| Line 162: | Line 149: | ||
{{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 | ||
}} | }} | ||
Revision as of 10:53, 21 March 2013
| Lie groups |
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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}}