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6
votes
0answers
69 views
Must nonunit in group algebra of free group generate proper two-sided ideal?
Let $F$ be a free group and $k$ be a field. If $x$ is an element of
the group algebra $k[F]$ that is not a unit (equivalently, that is not
a nonzero scalar multiple of an element of $F$), must the ...
2
votes
1answer
96 views
Units in a finite semisimple group algebra
Let $G$ be a finite group and $k$ a finite field, with the characteristic of $k$ not dividing the order of $G$. Then $kG$ is a finite semisimple group algebra with the interesting property that an ...
3
votes
1answer
76 views
Intersection of Maximal Left Ideals with Finite Dimensional Quotient
Let $\Gamma$ be a finitely generated group and let $A=\mathbb{C}[\Gamma]$ be the corresponding group algebra over $\mathbb{C}$. Let $X$ be the set of all maximal left ideals of $A$ and let $X_0=\{I ...
2
votes
0answers
159 views
(Non trivial) coidempotents(Co-$K$-theory)
I was interested to know about coalgebraic version of "Idempotents".
So I seached the web and I found the following interesting post :
...
2
votes
1answer
145 views
$Aut(\mathbb{Z}G)=?$ 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
...
7
votes
2answers
291 views
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 ...
10
votes
0answers
327 views
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 ${\bf Z}_p H$ ?
...
3
votes
0answers
650 views
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 ...
0
votes
0answers
120 views
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 ...
13
votes
1answer
495 views
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 ...
2
votes
2answers
154 views
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, ...
6
votes
2answers
994 views
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 ...
21
votes
3answers
2k views
Splitting the determinant polynomial into linear factors - a Dedekind problem
Here's the question in a nutshell. For some $n\in\mathbb N$, we consider the polynomial
$\det\left(\left(X_{i,j}\right) _ {1\leq i\leq n,\ 1\leq j\leq n}\right)\in\mathbb Z\left[X_{i,j}\mid 1\leq ...
0
votes
0answers
309 views
Is there a good reference for studying the ideal structure of group C* algebras?
Is there a good reference for studying the ideal structure of group C* algebras?
Thanks.
3
votes
2answers
416 views
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, ...
5
votes
2answers
697 views
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 ...
11
votes
3answers
953 views
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 ...
13
votes
3answers
1k views
Is the group von Neumann algebra construction functorial?
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 ...
