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edit approved Apr 30, 2016 at 12:33
Mahmood Al
edit approved Apr 30, 2016 at 12:33
Mahmood Al
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Hi! Let G,HLet $G$ and $H$ be discrete groups and f:G->H$f:G \rightarrow H$ be any homomorphism of these groups. I have three questions about it:

  1. howHow to prove the functoriality of the construction of universal C-algebra of discrete group (the existence of induced homomorphism C(G)$C^*$->C*algebra of discrete group (H)the existence of induced homomorphism $C^*(G) \to C^*(H)$)?

  2. howHow to prove that the construction of reduced C*$C^*$-algebra of discrete group is not functorial (I am especially interested in counterexamples) and in which case (I mean conditions for group homomorphism) it'll be functorial?

  3. letLet us consider the case when G = Z $G = \mathbb{Z}$ (integers) and H = Z/ nZ$H = \mathbb{Z}/ n\mathbb{Z}$. How to describe the kernel and the image of the induced homomorphism of group C* algebras$C^*$-algebras?

Hi! Let G,H be discrete groups and f:G->H be any homomorphism of these groups. I have three questions about it:

  1. how to prove the functoriality of the construction of universal C-algebra of discrete group (the existence of induced homomorphism C(G)->C*(H))?

  2. how to prove that the construction of reduced C*-algebra of discrete group is not functorial (I am especially interested in counterexamples) and in which case (I mean conditions for group homomorphism) it'll be functorial?

  3. let us consider the case when G = Z (integers) and H = Z/ nZ. How to describe the kernel and the image of the induced homomorphism of group C* algebras?

Let $G$ and $H$ be discrete groups and $f:G \rightarrow H$ be any homomorphism of these groups. I have three questions about it:

  1. How to prove the functoriality of the construction of universal $C^*$-algebra of discrete group (the existence of induced homomorphism $C^*(G) \to C^*(H)$)?

  2. How to prove that the construction of reduced $C^*$-algebra of discrete group is not functorial (I am especially interested in counterexamples) and in which case (I mean conditions for group homomorphism) it'll be functorial?

  3. Let us consider the case when $G = \mathbb{Z}$ (integers) and $H = \mathbb{Z}/ n\mathbb{Z}$. How to describe the kernel and the image of the induced homomorphism of group $C^*$-algebras?

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skripka
skripka
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The functoriality of group C* algebra structure

Hi! Let G,H be discrete groups and f:G->H be any homomorphism of these groups. I have three questions about it:

  1. how to prove the functoriality of the construction of universal C-algebra of discrete group (the existence of induced homomorphism C(G)->C*(H))?

  2. how to prove that the construction of reduced C*-algebra of discrete group is not functorial (I am especially interested in counterexamples) and in which case (I mean conditions for group homomorphism) it'll be functorial?

  3. let us consider the case when G = Z (integers) and H = Z/ nZ. How to describe the kernel and the image of the induced homomorphism of group C* algebras?