# Questions tagged [crossed-products]

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### A completely positive equivariant map $\varphi: A \to B$ induces a map on the full crossed products

Let $G$ be a discrete group. Let $(A,\alpha)$ and $(B,\beta)$ be $G$-$C^*$-algebras and $\varphi: A \to B$ be $G$-equivariant and completely positive. All crossed products in this post are full (= ...
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### commutative diagram with $K_{i+1}(A)\to K_i(A\rtimes_{\rho} \mathbb{R})$ (for $C^*$-algebras)

I have a question about a proof in Rosenberg and Schochet's paper "the Künneth theorem and the Universal Coefficient Theorem for Kasparov's generalized K-functor", proposition 2.6. First of all, the ... 305 views

### When is a crossed-product algebra a division algebra?

Let $L/K$ be a finite Galois extension with Galois group $G$. For every 2-cocycle $\gamma$ of $G$ with values in $L^\times$ there is the crossed-product $K$-algebra S(L,G,\gamma) = \bigoplus_{g\in ...
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### types of crossed product von Neumann algebras

Let $M$ be a type $II_1$ factor von Neumann algebra, and let $G$ be a discrete group acting on $M$ which is free and ergodic. Is the crossed product von Neumann algebra $M \rtimes G$ type $II_1$ ...
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### An unconventional definition of the $C^{*}$-algebraic reduced crossed product

Let $(A,G,\alpha)$ be a $C^{*}$-dynamical system, i.e., $A$ is a $C^{*}$-algebra, $G$ is a locally compact Hausdorff group and $\alpha$ is a strongly continuous action of $G$ on $A$ by ...
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What can be said about the following crossed product $C^*$-algebra? Let $A$ be a Kirchberg algebra with $K_0(A) = \mathbb{Q}$ and $K_1(A) = 0$. Consider the direct sum of $n$ copies of $A$, i.e. $B = ... 8 votes 2 answers 403 views ### Extending a$ * $-Representation of$ ({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 \... 3 votes 1 answer 259 views ### ‘Non-Induced’ Left Regular Representations of C^{*} $-Dynamical Systems In what follows, a ‘$ * $-representation’ always means a non-degenerate$ * $-representation. Let$ (\mathscr{A},G,\alpha) $be a$ C^{*} $-dynamical system, and let$ \pi: \mathscr{A} \to B(\mathcal{... 284 views

### States/functionals on crossed product C*-algebras

Let $A$ be a C*-algebra, $\alpha$ a strongly continuous automorphic action by a locally compact group $G$ on $A$, and consider the crossed product $A\rtimes_\alpha G$. I am looking for references ...