# Questions tagged [tensor-products]

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### Reverse the construction of a basis for a tensor product of vector spaces [closed]

If $V,W$ are infinite-dimensional vector spaces with basis {${v_i}$} and {${w_j}$} respectively it holds that $V\otimes W$ has as basis {${v_i⊗w_j}$}. What about the reciprocal? That is: if {${v_i}$} ...
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### Compute Frobenius inner product of two tensor-trains in terms of tensor contractions

Let $p\in\mathbb N$, $n\in\mathbb N^p$ and identify the Hilbert space tensor $\bigotimes_{k=1}^p\mathbb R^{n_k}$ with $\mathbb R^{n_1\times\cdots\times n_p}$ (equipped with the Euclidean inner product)...
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### Semisimplicity for tensor products of representations of finite groups

Let $G$ be a group and $k$ a field of characteristic $p>0$. Let $$\rho_i: G\to GL(V_i),~ i=1,2$$ be two finite-dimensional semisimple $k$-representations of $G$, with $\dim(V_1)+\dim(V_2)<p+2.$ ...
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### Completed tensor product is exact

In the beginning of the 7th chapter of the book "Spectral theory and analytic geometry over non-Archimedean fields" by Vladimir Berkovich one can find the phrase "...tensor product functor is exact on ...
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### Exterior paring of groups

The non-abelian tensor square $G\otimes G$ of a group $G$ is defined as a group generated by the words $g\otimes h$, $g,h \in G$ related to the conditions $gg'\otimes h=(^gg'\otimes ^gh)(g\otimes h)$...
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### What is the suitable tensor product for Holder spaces

We know that for $X\subset\mathbb R^m,Y\subset\mathbb R^n$ open, then $C^0(\bar X\times\bar Y)=C^0(\bar X)\hat\otimes_\varepsilon C^0(\bar Y)$ where $V\hat\otimes_\varepsilon W$ is the injective ...
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### Ideal structure of a tensor product of certain algebras

I would be grateful if anyone could give me a reference regarding the following question. Suppose that $A$ and $B$ are two unital prime algebras over a field $F$ whose center consists of scalar ...
Let's work in the category $R$-${\sf mod}$, for concreteness. I know that one can see the modules ${\rm Ext}^n_R(M,N)$ as modules of equivalence classes of $n$-extensions of $M$ by $N$ (Yoneda ...