Representation of $SO(3)$ [on hold]Do all Groups have a representation?Lie bracket as defining element for transformationsIs trace of regular representation in Lie group a delta function?Is trace of regular representation in Lie group a delta function?Groups without matrix representation?Representation theory definition confusionstandard representation for symmetric groups motivationSplitting Field in Group Representation and PolynomialDimensionality of representationsGroup theory and Quantum mechanics
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Representation of $SO(3)$ [on hold]
Do all Groups have a representation?Lie bracket as defining element for transformationsIs trace of regular representation in Lie group a delta function?Is trace of regular representation in Lie group a delta function?Groups without matrix representation?Representation theory definition confusionstandard representation for symmetric groups motivationSplitting Field in Group Representation and PolynomialDimensionality of representationsGroup theory and Quantum mechanics
$begingroup$
I am confused about varies definitions of representation of a group, for example consider the rotation group $SO(3)$. For $SO(3)$ what is its representation?
Vectors and all tensors that transform under $SO(3)$ is called representation of $SO(3)$ or the metric elements of $SO(3)$ which corresponds to transformation of coordinate is called representation of $SO(3)$. Which one is right?
group-theory representation-theory lie-groups
edited 2 days ago
Christoph
12.5k1642
asked 2 days ago
robinrobin
183
$endgroup$
put on hold as unclear what you're asking by José Carlos Santos, Christoph, Song, Ramiro, Paul Frost 2 days ago
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
I am confused about varies definitions of representation of a group, for example consider the rotation group $SO(3)$. For $SO(3)$ what is its representation?
Vectors and all tensors that transform under $SO(3)$ is called representation of $SO(3)$ or the metric elements of $SO(3)$ which corresponds to transformation of coordinate is called representation of $SO(3)$. Which one is right?
group-theory representation-theory lie-groups
edited 2 days ago
Christoph
12.5k1642
asked 2 days ago
robinrobin
183
$endgroup$
put on hold as unclear what you're asking by José Carlos Santos, Christoph, Song, Ramiro, Paul Frost 2 days ago
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
There is not "the representation of a group". A representation of a group $G$ is a vector space $V$ on which $G$ acts by endomorphisms. For a given $G$, there are many different representations.
$endgroup$
– Christoph
2 days ago
2
$begingroup$
Neither of those are a good definition. Look up the general definition (for an abstract group) first.
$endgroup$
– Tobias Kildetoft
2 days ago
add a comment |
$begingroup$
I am confused about varies definitions of representation of a group, for example consider the rotation group $SO(3)$. For $SO(3)$ what is its representation?
Vectors and all tensors that transform under $SO(3)$ is called representation of $SO(3)$ or the metric elements of $SO(3)$ which corresponds to transformation of coordinate is called representation of $SO(3)$. Which one is right?
group-theory representation-theory lie-groups
edited 2 days ago
Christoph
12.5k1642
asked 2 days ago
robinrobin
183
$endgroup$
I am confused about varies definitions of representation of a group, for example consider the rotation group $SO(3)$. For $SO(3)$ what is its representation?
Vectors and all tensors that transform under $SO(3)$ is called representation of $SO(3)$ or the metric elements of $SO(3)$ which corresponds to transformation of coordinate is called representation of $SO(3)$. Which one is right?
group-theory representation-theory lie-groups
group-theory representation-theory lie-groups
edited 2 days ago
Christoph
12.5k1642
asked 2 days ago
robinrobin
183
edited 2 days ago
Christoph
12.5k1642
asked 2 days ago
robinrobin
183
edited 2 days ago
Christoph
12.5k1642
edited 2 days ago
Christoph
12.5k1642
edited 2 days ago
Christoph
12.5k1642
12.5k1642
asked 2 days ago
robinrobin
183
asked 2 days ago
robinrobin
183
asked 2 days ago
robinrobin
183
183
put on hold as unclear what you're asking by José Carlos Santos, Christoph, Song, Ramiro, Paul Frost 2 days ago
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as unclear what you're asking by José Carlos Santos, Christoph, Song, Ramiro, Paul Frost 2 days ago
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
There is not "the representation of a group". A representation of a group $G$ is a vector space $V$ on which $G$ acts by endomorphisms. For a given $G$, there are many different representations.
$endgroup$
– Christoph
2 days ago
2
$begingroup$
Neither of those are a good definition. Look up the general definition (for an abstract group) first.
$endgroup$
– Tobias Kildetoft
2 days ago
add a comment |
$begingroup$
There is not "the representation of a group". A representation of a group $G$ is a vector space $V$ on which $G$ acts by endomorphisms. For a given $G$, there are many different representations.
$endgroup$
– Christoph
2 days ago
2
$begingroup$
Neither of those are a good definition. Look up the general definition (for an abstract group) first.
$endgroup$
– Tobias Kildetoft
2 days ago
$begingroup$
There is not "the representation of a group". A representation of a group $G$ is a vector space $V$ on which $G$ acts by endomorphisms. For a given $G$, there are many different representations.
$endgroup$
– Christoph
2 days ago
$begingroup$
There is not "the representation of a group". A representation of a group $G$ is a vector space $V$ on which $G$ acts by endomorphisms. For a given $G$, there are many different representations.
$endgroup$
– Christoph
2 days ago
2
2
$begingroup$
Neither of those are a good definition. Look up the general definition (for an abstract group) first.
$endgroup$
– Tobias Kildetoft
2 days ago
$begingroup$
Neither of those are a good definition. Look up the general definition (for an abstract group) first.
$endgroup$
– Tobias Kildetoft
2 days ago
add a comment |
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$begingroup$
There is not "the representation of a group". A representation of a group $G$ is a vector space $V$ on which $G$ acts by endomorphisms. For a given $G$, there are many different representations.
$endgroup$
– Christoph
2 days ago
2
$begingroup$
Neither of those are a good definition. Look up the general definition (for an abstract group) first.
$endgroup$
– Tobias Kildetoft
2 days ago