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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.
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 …
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 …
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.
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 …
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 …
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, …
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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