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OK, maybe this is asking too much, hopefully not.

I'm trying to understand the connection between all of these constructions. I wonder if a summary about these interrelationship can be given.

If I understand what I'm reading, there is a connection between finite groups and algebras, though I think I'm confused between what objects are involved in each and what each acts upon if anything. And I understand that there is a conserved quantity for every symmetry, but this is only for symmetries of Action integral, right? What I'm not sure about, though, is whether there is a connection between algebras and commutation relations. Any insight you could give in these areas would be appreciated. Thanks.

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# Symmetry Groups Algebras Commutators Conserved Quantities

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