Notes for wClips-120314/0:11:34 - Revision history

Drorbn at 00:30, 20 March 2012

2012-03-20T00:30:45Z

← Older revision		Revision as of 20:30, 19 March 2012
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	It is great to know the relationship with Lie bialgebras, as it is extremely relevant for the study of ${\mathcal A}^v$. Yet it is also good to know that $I{\mathfrak g}$ has a much simpler definition, that avoids some of the complexity. Namely, $I{\mathfrak g}$ is the semi-direct product ${\mathfrak g}^\star\rtimes{\mathfrak g}$, where ${\mathfrak g}$ acts on its dual ${\mathfrak g}^\star$ using the coadjoint action. The metric on $I{\mathfrak g}$ need not ever be explicitly used, yet it is the metric associated with the a norm on $I{\mathfrak g}$, which is simply the contraction map of ${\mathfrak g}^\star$ and ${\mathfrak g}$. This definition appears roughly starting at minute 44:00 of this video.		It is great to know the relationship with Lie bialgebras, as it is extremely relevant for the study of ${\mathcal A}^v$. Yet it is also good to know that $I{\mathfrak g}$ has a much simpler definition, that avoids some of the complexity. Namely, $I{\mathfrak g}$ is the semi-direct product ${\mathfrak g}^\star\rtimes{\mathfrak g}$, where ${\mathfrak g}$ acts on its dual ${\mathfrak g}^\star$ using the coadjoint action. The metric on $I{\mathfrak g}$ need not ever be explicitly used, yet it is the metric associated with the a norm on $I{\mathfrak g}$, which is simply the contraction map of ${\mathfrak g}^\star$ and ${\mathfrak g}$. This definition appears roughly starting at minute 44:00 of this video. --[[User:Drorbn\|Drorbn]] 20:30, 19 March 2012 (EDT)

Drorbn at 00:30, 20 March 2012

2012-03-20T00:30:22Z

← Older revision		Revision as of 20:30, 19 March 2012
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	It is great to know the relationship with Lie bialgebras, as it is extremely relevant for the study of ${\mathcal A}^v$. Yet it is also good to know that $I{\mathfrak g}$ has a much simpler definition, that avoids some of the complexity. Namely, $I{\mathfrak g}$ is the semi-direct product ${\mathfrak g}^\star\rtimes{\mathfrak g}$, where ${\mathfrak g}$ acts on its dual ${\mathfrak g}^\star$ using the coadjoint action. The metric on $I{\mathfrak g}$ need not ever be explicitly used, yet it is the metric associated with the a norm on $I{\mathfrak g}$, which is simply the contraction map of ${\mathfrak g}^\star$ and ${\mathfrak g}$. ~~--[[User:Drorbn\|Drorbn]]~~ ~~18:44,~~ 19 ~~March~~ ~~2012~~ ~~(EDT)~~		It is great to know the relationship with Lie bialgebras, as it is extremely relevant for the study of ${\mathcal A}^v$. Yet it is also good to know that $I{\mathfrak g}$ has a much simpler definition, that avoids some of the complexity. Namely, $I{\mathfrak g}$ is the semi-direct product ${\mathfrak g}^\star\rtimes{\mathfrak g}$, where ${\mathfrak g}$ acts on its dual ${\mathfrak g}^\star$ using the coadjoint action. The metric on $I{\mathfrak g}$ need not ever be explicitly used, yet it is the metric associated with the a norm on $I{\mathfrak g}$, which is simply the contraction map of ${\mathfrak g}^\star$ and ${\mathfrak g}$. This definition appears roughly starting at minute 44:00 of this video.

Drorbn at 22:44, 19 March 2012

2012-03-19T22:44:23Z

New page

It is great to know the relationship with Lie bialgebras, as it is extremely relevant for the study of ${\mathcal A}^v$. Yet it is also good to know that $I{\mathfrak g}$ has a much simpler definition, that avoids some of the complexity. Namely, $I{\mathfrak g}$ is the semi-direct product ${\mathfrak g}^\star\rtimes{\mathfrak g}$, where ${\mathfrak g}$ acts on its dual ${\mathfrak g}^\star$ using the coadjoint action. The metric on $I{\mathfrak g}$ need not ever be explicitly used, yet it is the metric associated with the a norm on $I{\mathfrak g}$, which is simply the contraction map of ${\mathfrak g}^\star$ and ${\mathfrak g}$. --[[User:Drorbn|Drorbn]] 18:44, 19 March 2012 (EDT)