Definition:Equivalent Linear Representations
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Definition
Let $ \struct {G, \cdot}$ be a group.
Consider two linear representations $\rho: G \to \GL V$ and $\rho': G \to \GL W$ of $G$.
Then $\rho$ and $\rho'$ are called equivalent (linear representations) if and only if their correspondent $G$-modules using Correspondence between Linear Group Actions and Linear Representations are isomorphic.
This has to be rewritten. In particular: above line needs rewriting, but I can't come up with a suitable replacement You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by doing so. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Rewrite}} from the code. |
This article, or a section of it, needs explaining. In particular: The "isomorphic" link goes to a generic "abstract algebra" page, but I believe no actual definition has been made for an isomorphism between two G-modules. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code. |