Difference between revisions of "Template:Lie groups"
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imported>UtherSB m (Undoing my mistake. Have added disambiguation on symplectic group page.) |
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| − | {{Sidebar with collapsible lists | + | <includeonly>{{Sidebar with collapsible lists |
| name = Lie groups | | name = Lie groups | ||
| − | | | + | | class = plainlist |
| − | | imagestyle = | + | | pretitlestyle = font-size:8pt; <!--font-weight:none--> padding-bottom:0.3em |
| − | | image = [[File:E8Petrie.svg|frameless|180px | + | | pretitle = [[Group theory]] {{arrow/core|size=20}} [[Lie groups]] |
| − | | | + | | title = [[Lie groups]] |
| − | | expanded = {{{expanded|{{{1|}}}}}} | + | | imagestyle = display:block;margin:0.4em 0 0.9em |
| + | | image = [[File:E8Petrie.svg|frameless|180px|link=E8 (mathematics)]] | ||
| + | | 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 |
| − | + | | list1title = [[Classical group|Classical]] | |
| − | + | | list1 = | |
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* [[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'') | ||
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* [[Special unitary group|Special unitary]] SU(''n'') | * [[Special unitary group|Special unitary]] SU(''n'') | ||
* [[Symplectic group|Symplectic]] Sp(''n'') | * [[Symplectic group|Symplectic]] Sp(''n'') | ||
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| − | + | | list3name = simple | |
| − | + | | list3title = [[Simple Lie group|Simple]] | |
| − | + | | list3class = hlist | |
| − | | list3name = | + | | list3 = |
| − | | list3title = [[Simple Lie group]] | ||
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* [[List of simple Lie groups]] | * [[List of simple Lie groups]] | ||
| − | + | <div style="margin-top:0.25em;line-height:1.1em"> ''Classical'' | |
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* [[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'' | |
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* [[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> | |
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| − | < | ||
| − | | list4name = | + | | list4name = other |
| − | | list4title = [[Table of Lie groups|Other | + | | list4title = [[Table of Lie groups|Other]] |
| − | | list4 = | + | | list4class = hlist |
| + | | list4 = | ||
* [[Circle group|Circle]] | * [[Circle group|Circle]] | ||
* [[Lorentz group|Lorentz]] | * [[Lorentz group|Lorentz]] | ||
* [[Poincaré group|Poincaré]] | * [[Poincaré group|Poincaré]] | ||
| − | * [[Conformal group]] | + | * [[Conformal group|Conformal]] |
* [[Diffeomorphism]] | * [[Diffeomorphism]] | ||
* [[Loop group|Loop]] | * [[Loop group|Loop]] | ||
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| − | | list5name = | + | | list5name = algebras |
| − | | list5title = [[Lie algebra]]s | + | | list5title = [[Lie algebra|Algebra]]s |
| − | | list5 = <div class=" | + | | list5 = <div class="hlist" style="margin-bottom:0.4em"> |
| + | * [[Simple Lie algebra|Simple]] | ||
* [[Exponential map (Lie theory)|Exponential map]] | * [[Exponential map (Lie theory)|Exponential map]] | ||
| − | * | + | * [[Adjoint representation]] |
| − | * | + | ** [[Adjoint representation|group]] |
| + | ** [[Adjoint endomorphism|algebra]] | ||
| + | * [[Killing form]] | ||
| + | * [[Index of a Lie algebra|Index]] | ||
* [[Lie point symmetry]] | * [[Lie point symmetry]] | ||
| − | + | </div> ''[[Semisimple Lie algebra|Semisimple]]'' | |
| − | </div> | + | <div class="hlist" style="margin-top:0.15em;border-top:1px solid #aaa"> |
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* [[Dynkin diagram]]s | * [[Dynkin diagram]]s | ||
* [[Cartan subalgebra]] | * [[Cartan subalgebra]] | ||
| − | * | + | * [[Root system]] |
| − | * | + | * [[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> | </div> | ||
| − | + | | list6name = homogeneous | |
| − | + | | list6title = [[Homogeneous space]]s | |
| − | + | | list6 = | |
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* [[Borel–de Siebenthal theory|Closed subgroup]] | * [[Borel–de Siebenthal theory|Closed subgroup]] | ||
* [[Parabolic subgroup]] | * [[Parabolic subgroup]] | ||
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* [[Hermitian symmetric space]] | * [[Hermitian symmetric space]] | ||
* [[Restricted root system]] | * [[Restricted root system]] | ||
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| − | + | | list7name = representation | |
| + | | list7title = [[Representation theory]] | ||
| + | | list7class = hlist | ||
| + | | list7 = | ||
| + | * [[Representation of a Lie group|Lie group]] | ||
| + | * [[Lie algebra representation|Lie algebra]] | ||
| − | | | + | | list8name = physics |
| − | | | + | | list8title = Lie groups in [[physics]] |
| − | | | + | | list8 = |
| − | * [[Particle physics and representation theory]] | + | * {{longitem|style=padding:0.3em 0 0.2em|[[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]] | ||
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| + | | list9name = people | ||
| + | | list9title = People | ||
| + | | list9class = hlist | ||
| + | | list9 = | ||
| + | * [[Sophus Lie]] | ||
| + | * [[Henri Poincaré]] | ||
| + | * [[Wilhelm Killing]] | ||
| + | * [[Élie Cartan]] | ||
| + | * [[Hermann Weyl]] | ||
| + | * [[Claude Chevalley]] | ||
| + | * [[Harish-Chandra]] | ||
| + | * [[Armand Borel]] | ||
| − | | | + | | belowstyle = margin-top:0; border:none; padding-top:0 |
| below = | | below = | ||
* [[Table of Lie groups]] | * [[Table of Lie groups]] | ||
}}<noinclude> | }}<noinclude> | ||
| − | + | {{Documentation | |
| − | {{ | + | | content = {{Lie groups}} |
| − | + | {{Collapsible lists option | |
| − | + | | listnames = {{hlist |classical |simple |other |algebras |homegeneous |representation |physics |people}} | |
| + | | example = semi-simple | ||
}} | }} | ||
[[Category:Mathematics sidebar templates]] | [[Category:Mathematics sidebar templates]] | ||
[[Category:Physics sidebar templates]] | [[Category:Physics sidebar templates]] | ||
| − | + | }}</noinclude> | |
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| − | </noinclude> | ||