# Tagged Questions

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### (Non trivial) coidempotents(Co-$K$-theory)

I was interested to know about coalgebraic version of "Idempotents". So I seached the web and I found the following interesting post : http://math.stackexchange.com/questions/689322/co-idempotents-...
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### $Aut(\mathbb{Z}G)=?$ for $G=\mathbb{Z}^2\rtimes_n\mathbb{Z}$

I am interested in the automorphism group of the group ring $\mathbb{Z}G$ for some noncommutative group $G$ of the form $\mathbb{Z}^2\rtimes_n\mathbb{Z}$, say \mathbb{Z}^2\rtimes_n\mathbb{Z}=\...
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### Are the reduced group Von Neumann algebra/ Group $C^{\ast}$ algebra functorial in the case of LCH groups

Let $G$ be a LCH group and $\mu$ be its left Haar measure. Call $\lambda_G : G \to U(L_2(G,\mu))$ the left regular representation. We can define the reduced $C^{\ast}$ algebra and reduced Von Neumann ...
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### Group rings isomorphic over F_p, but not over Z_p ?

Suppose given a prime $p$. Question: Do there exist finite groups $G$ and $H$ such that ${\bf F}_p G$ is isomorphic to ${\bf F}_p H$, but such that ${\bf Z}_p G$ is not isomorphic to ${\bf Z}_p H$ ? ...
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### Is the radical of a homogeneous ideal homogeneous?

Let $S$ be an $M$-graded $R$-algebra, where $M$ is some monoid, and $I\subset S$ an homogeneous ideal. The original, naïve, question, was: is it true that $\sqrt{I}$ is homogeneous? In this generality,...
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### Are all of compact support functions of $A(G)$ in its abstract Segal algebras?

Let $G$ be a locally compact group. We know that if $G$ is abelian and $\cal F$ implies the Fourier transform, for every Segal algebra of $G$ say $S^1(G)$, ${\cal F}S^1(G)$ is an abstract Segal ...
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### Does $\mathbb{K}[G]\simeq\mathbb{K}[H]$ for some field $\mathbb{K}$ of characteristic $p$, imply $\mathbb{F}_p[G]\simeq\mathbb{F}_p[H]$?

Due to the first (and very helpful) answer I received, I've reformulated the question a little: $G$ and $H$ are now assumed to be $p$-groups. Let $p$ be a prime, and let $\mathbb{F}_p$ be the field ...
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### vanishing of certain product in group algebra

Let $G$ be a finite abelian group. When $\prod_{g\in G\setminus 1} (1-g)$ vanishes in (say, complex) group algebra of $G$? It is easy to see that for cyclic group $G$ such product does not vanish, ...
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### Amenability of an “almost Hamiltonian” group

Here is another interesting question that I can't answer on my own. Let $G$ be a countable, discrete group such that for any subgroup $H$ of $G$ and any element $s$ of $G$ we have $[H : sHt]$ is ...
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### Reference for von Neumann algebras coming from a group algebra twisted by a 2-cocycle?

I am looking at a von Neumann algebra constructed from a discrete group and a 2-cocylce. Does someone know some good references (article, book)? It would be very helpful for me. To be more precise, ...
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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 ...
### The difference between $l^1(G)$ and the reduced group $C^*$ algebra $C_r^*(G)$
Let $G$ be a group and $l^2(G)$ the Hilbert space on $G$. The complex group algebra $CG$ can be imbedded in $B(l^2(G))$, the set of all bounded linear operators, by left translation. The reduced group ...
Let $G$ be a group and $CG$ the complex group algebra over the field $C$ of complex number. The group von Neumann algebra $NG$ is the completion of $CG$ wrt weak operator norm in $B(l^2(G))$, the set ...