# Questions tagged [tensor-products]

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### Can we test if an abelian group is finitely generated by taking tensor product?

If $A$ is a finitely generated abelian group, then we know that for all fields $k$, the tensor product $A\otimes_{\mathbb{Z}}k$ is finite dimensional as a $k$-vector space. The converse is not true, ...
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### Stokes' lemma / Yoneda's theorem

Definition: Write SmoothOrientedManifold for the category of smooth oriented real manifolds. Definition: Write ChainComplex for the category of chain complexes, and write $\otimes$ for the tensor ...
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### Irreducible tensor product representations in finite simple groups

$\DeclareMathOperator\GL{GL}\DeclareMathOperator\PSL{PSL}\DeclareMathOperator\PSp{PSp}\DeclareMathOperator\PSU{PSU}$Background: A representation $\rho: G \to \GL(V)$ of a group $G$ on a (complex) ...
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### Tensor product of finite extensions of $\mathbb{Q}_p$

Consider the tensor product of finite extensions of a field $F$ of characteristic zero. (I am interested in the case $F=\mathbb{Q}_p$.) $(1)$ If $M$ is a finite Galois extension of $F$ with Galois ...
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1 vote
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### Vanishing (infinite) tensor products

Since the advent of free probabilities and QFT, infinite tensor products of $R$-associative algebras with units has become more familiar to the working mathematician. Starting from the (permuting) ...
• 3,726
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### Combination of simple tensors - II

This is a follow-up question to Combination of simple tensors. I am interested in devising an alternative norm (I mean, other than the usual $\pi$ or $\epsilon$ norms) in the tensor product of two ...
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