What does embedding a group into another group mean for the group generators? Can you please explain with an example. I would like to know what it means for $SU(3)$ to be embedded in $SU(3)\times SU(3)$ in terms of the generators (in matrix form).
2026-03-26 01:28:08.1774488488
Embedding of a subgroup into a group
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This is an answer to the question you've asked, but probably not the question you are trying to ask.
The concept is straightforward: an embedding is just an injective homomorphism. Any particular embedding maps the generators to wherever they go. Asking about the "leftover generators" in the codomain makes no sense.
Your comment seems to ask about "the embedding". There are many. If there's a particular one you care about (presumably because of its origin in physics) you should edit the question to tell us what it is, and ask a partcular question that puzzles you.