Theorem
Maschke's Theorem for Compact Groups
Every finite-dimensional continuous representation (Definition~Group Representation) of a compact Lie group (Definition~Compactness) over $\mathbb{R}$ or $\mathbb{C}$ is completely reducible (Definition~Complete Reducibility).
Dependency Graph
flowchart LR
classDef current fill:#6366f1,color:#fff,stroke:#4f46e5
nca6bd350["Representation"]
n5d29db29["Compactness"]
na4ca6986["Complete Reducibility"]
n692f1650["Maschke's Theorem for Compact Groups"]:::current
n59a974c0["Regular Representation"]
nb96526a2["Remark"]
n3b157f10["Dimension Formula"]
nca6bd350 --> n692f1650
n5d29db29 --> n692f1650
na4ca6986 --> n692f1650
n692f1650 --> n59a974c0
n692f1650 --> nb96526a2
n692f1650 --> n3b157f10
click nca6bd350 "../objects/ca6bd350.html" "_self"
click n5d29db29 "../objects/5d29db29.html" "_self"
click na4ca6986 "../objects/a4ca6986.html" "_self"
click n59a974c0 "../objects/59a974c0.html" "_self"
click nb96526a2 "../objects/b96526a2.html" "_self"
click n3b157f10 "../objects/3b157f10.html" "_self"