군,group

Difference between r1.11 and the current

@@ -1,7 +1,7 @@

#noindex
## =군,group =,group .
WtEn:group

----

[[군론,group_theory]] =군론,group_theory =,group_theory . 군론 group_theory
{

@@ -11,6 +11,21 @@

WpEn:Group_theory

[[스핀,spin]] 설명 video의 일부. 2분동안 군 매우 간략 설명.

https://youtu.be/pYeRS5a3HbE?&t=120

[[스피너,spinor]] 설명 video에서,

SO(n) - https://youtu.be/b7OIbMCIfs4?t=1371 .... the algebra of [[회전,rotation]]s. // rel [[직교군,orthogonal_group]]

SU(n) - https://youtu.be/b7OIbMCIfs4?t=2028 // rel [[unitary_group]]

{

SU(2) is complex generalization of SO(2).

|| SO(2) || SU(2) ||

||$R=\begin{bmatrix}a&-b\\b&a\end{bmatrix}$ ||$U=\begin{bmatrix}\alpha&-\beta^*\\\beta&\alpha^*\end{bmatrix}$ ||

||$a,b\in\mathbb{R},\; a^2+b^2=1$ ||$\alpha,\beta\in\mathbb{C},\; |\alpha|^2 + |\beta|^2 = 1$ ||

||$\det R = 1$ (special) ||$\det U = 1$ (special) ||

||$R^{-1} = R^T$ (orthogonal) ||$U^{-1} = U^{\dagger}$ (unitary) ||

}

Sub:
[[combinatorial_group_theory]]

@@ -21,7 +36,11 @@

----
Sub:

[[호모토피군,homotopy_group]]

[[호모토피군,homotopy_group]] - [[호모토피,homotopy]]

[[몫군,quotient_group]] - [[몫,quotient]]

[[로런츠_군,Lorentz_group]]

[[직교군,orthogonal_group]]

----
<<tableofcontents>>
= Sub =

군론,group_theory =군론,group_theory =,group_theory . 군론 group_theory
{

스핀,spin 설명 video의 일부. 2분동안 군 매우 간략 설명.
https://youtu.be/pYeRS5a3HbE?&t=120

스피너,spinor 설명 video에서,
SO(n) - https://youtu.be/b7OIbMCIfs4?t=1371 .... the algebra of 회전,rotations. // rel 직교군,orthogonal_group
SU(n) - https://youtu.be/b7OIbMCIfs4?t=2028 // rel unitary_group
{
SU(2) is complex generalization of SO(2).

SO(2)	SU(2)
$\displaystyle R=\begin{bmatrix}a&-b\\b&a\end{bmatrix}$	$\displaystyle U=\begin{bmatrix}\alpha&-\beta^\\\beta&\alpha^\end{bmatrix}$
$\displaystyle a,b\in\mathbb{R},\; a^2+b^2=1$	$\displaystyle \alpha,\beta\in\mathbb{C},\; \|\alpha\|^2 + \|\beta\|^2 = 1$
$\displaystyle \det R = 1$ (special)	$\displaystyle \det U = 1$ (special)
$\displaystyle R^{-1} = R^T$ (orthogonal)	$\displaystyle U^{-1} = U^{\dagger}$ (unitary)

}

Sub:
combinatorial_group_theory

Up: 군,group 이론,theory
분야 추상대수,abstract_algebra?

} // group theory ....

Sub:
호모토피군,homotopy_group - 호모토피,homotopy
몫군,quotient_group - 몫,quotient
로런츠_군,Lorentz_group
직교군,orthogonal_group

Contents

1.1. trivial group / zero group
1.2. additive group
1.3. multiplicative group 곱셈군
1.4. Lie group 리 군
1.5. 가환군 commutative grup = 아벨 군 abelian group
1.6. ADDHERE new group
1.7. ADDHERE new group
1.8. ADDHERE new group
1.9. ADDHERE new group
1.10. ADDHERE new group
1.11. ADDHERE new group
1.12. ADDHERE new group
1.13. ADDHERE new group
1.14. ADDHERE new group

1. Sub ¶

1.1. trivial group / zero group ¶

trivial_group = zero_group (we)
trivial_group 의 한 예가 zero_group (MW)
https://mathworld.wolfram.com/TrivialGroup.html
https://mathworld.wolfram.com/ZeroGroup.html
https://en.wikipedia.org/wiki/Trivial_group

cmp:
trivial_monoid
trivial_ring

trivial group zero group

1.2. additive group ¶

https://mathworld.wolfram.com/AdditiveGroup.html
module, abstract_vector_spaces, 대수,algebra는 모두 additive groups.

덧셈,addition

additive group ?

1.3. multiplicative group 곱셈군 ¶

곱셈군
multiplicative group
곱셈군,multiplicative_group — curr at 프로덕트,product?action=highlight&value=multiplicative_group

1.4. Lie group 리 군 ¶

리_군,Lie_group =리_군,Lie_group =,Lie_group . 리_군 Lie_group

Lie group
리 군

//mw
{
매끄러운다양체,smooth_manifold
}

MKL
리_대수,Lie_algebra

Lie_group = https://en.wiktionary.org/wiki/Lie_group
{
Up(Hyper):
topological_group ...

topological_group = http://en.wiktionary.org/wiki/topological_group

Sub(Hypo):
circle_group ...

circle_group = http://en.wiktionary.org/wiki/circle_group
Moebius_group ...

Moebius_group = http://en.wiktionary.org/wiki/Moebius_group
}

https://mathworld.wolfram.com/LieGroup.html
https://mathworld.wolfram.com/Lie-TypeGroup.html

리 군 = https://namu.wiki/w/리 군
[https]

[https]

수학백과: 리 군

Lie_group = https://en.wikipedia.org/wiki/Lie_group

리_군 = https://ko.wikipedia.org/wiki/리_군

https://everything2.com/title/lie group
(very long)

https://ncatlab.org/nlab/show/Lie group

https://encyclopediaofmath.org/wiki/Lie_group
/// cf.
{
https://encyclopediaofmath.org/wiki/Lie_group,_local - local analytic group // analytic_group
https://encyclopediaofmath.org/wiki/Lie_transformation_group
https://encyclopediaofmath.org/wiki/Lie_group,_p-adic
https://encyclopediaofmath.org/wiki/Lie_group,_semi-simple
https://encyclopediaofmath.org/wiki/Lie_group,_compact
}

Lie group
Lie+group

1.5. 가환군 commutative grup = 아벨 군 abelian group ¶

가환군,commutative_group
아벨_군,abelian_group

1.6. ADDHERE new group ¶

1.7. ADDHERE new group ¶

1.8. ADDHERE new group ¶

1.9. ADDHERE new group ¶

1.10. ADDHERE new group ¶

1.11. ADDHERE new group ¶

1.12. ADDHERE new group ¶

1.13. ADDHERE new group ¶

1.14. ADDHERE new group ¶

2. MKL ¶

마그마,magma
그루포이드,groupoid - curr at 마그마,magma
모노이드,monoid
환,ring
체,field
module ( 가군,module 모듈,module ) - curr at 추상대수,abstract_algebra 에서 algebraic_structure 편집중인 곳

Up:
추상대수,abstract_algebra > 대수구조,algebraic_structure