# Questions tagged [crossed-products]

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### Non-existence of projections in crossed product

If $X$ is a smooth manifold on which a Lie group $G$ acts properly and cocompactly (meaning $X/G$ is compact), then one can find a compactly support cut-off function $c:X\rightarrow\mathbb{R}$ such ...
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### Crossed products and unitaries implementing $\mathbb{Z}_n$-actions

I'm working through Li's and Barlak's Cartan Subalgebras and the UCT Problem but I'm stuck at one of the simpler proofs of the paper. On page 9 they deal with masas (maximal abelian subalgebras) of a ...
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### Classification of quasitriangular Hopf algebras

The classification of hopf algebras is a big and open problem, containing various subproblems (such as: the classification of groups, of Lie algebras, the study of special classes such as (co)...
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### Extending a $*$-Representation of $({C_{c}}(G,\mathscr{A}),\star,^{*})$ to a $*$-Representation of $\mathscr{A} \rtimes_{\alpha} G$

Let $(\mathscr{A},G,\alpha)$ be a $C^{*}$-dynamical system, and consider the twisted convolution $*$-algebra $({L^{1}}(G,\mathscr{A}),\star,^{*})$ defined by \begin{align*} \forall \phi,\psi \...
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### For a separable v-N algebra M, how to see $M \rtimes \mathbb{R}$ as a subalgebra of $M \otimes B(L^2)$?

For a v-N algebra $M$ acting as bounded operators on a separable Hilbert space $H$, how to see $M \rtimes \mathbb{R}$ as a subalgebra of $M \otimes B(L^2(\mathbb{R})$? Why I am confused is because \$...
2answers
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### Universal characterization and explicit description of elements of the group von Neumann algebra and the crossed product

Group von Neumann algebras and crossed products for a locally compact group G can be constructed in many different ways. For example, one can take the von Neumann algebra generated by certain ...