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Sep 28, 2024 · Let $G$ be a group with some completely reducible finite-dimensional representations $V,W$, and let $\\mathbf{1}$ be the trivial irreducible representation. I'm ...
Nov 13, 2015 · A symbol I have in my math homework looks like a ~ above a =. (That is, $\\cong$.) What does this mean? I'm studying Congruency at the moment if that helps.
Aug 22, 2023 · Q1: Yes, this is the definition of the determinant of a one-dimensional vector space. Q2: Yes, the dual of the trivial line bundle is the trivial line bundle (for instance, use that a line …
In geometry, $\cong$ means congruence of figures, which means the figures have the same shape and size. (In advanced geometry, it means one is the image of the other under a mapping known …
This approach uses the chinese remainder lemma and it illustrates the 'unique factorization of ideals' into products of powers of maximal ideals in Dedekind domains: It follows $-1 \cong 10-1 …
Nov 28, 2024 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation …
Jan 1, 2025 · I went through several pages on the web, each of which asserts that $\operatorname {Aut} A_n \cong \operatorname {Aut} S_n \; (n\geq 4)$ or an equivalent statement without proof, …
In mathematical notation, what are the usage differences between the various approximately-equal signs '≈', '≃', and '≅'? The Unicode standard lists all of them inside the Mathematical Operators …
Feb 22, 2021 · Then $\alpha \times \beta \cong \alpha \otimes \beta$, where $\alpha \times \beta$ is in anti-lexicographic order. I have come up with one proof, and I would like to get it validated.
Aug 9, 2025 · Are you sure that $\left\ {\pmatrix { a & b\\0&a^2}\mid a,b\in K, a\ne 0\right\}\cong (K,+)$?
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