$G$ is a compact Lie group with closed subgroup $H$ and $\mathscr{T}(G),\mathscr{T}(H)$ are the sets of their representative functions respectively (with real or complex representation). If the restriction map $i:\mathscr{T}(G) \rightarrow \mathscr{T}(H)$ is an isomorphism as algebra, then is $H=G$?
2026-05-06 00:14:32.1778026472
The isomorphism of representive functions
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