All Questions
Tagged with ra.rings-and-algebras oa.operator-algebras
66 questions
7
votes
1
answer
250
views
$K_0$ group of graph underlying an approximately finite (AF) C* algebra
Say we have an AF C* algebra $A$ described by some Bratteli diagram $E$. If $M_\infty (A)=\displaystyle{\lim_\rightarrow M_n(A)}$ and $P(A)$ are the projections in this algebra, we know that $K_0(A)^+=...
- 125
3
votes
1
answer
309
views
Metrics and completions on the direct limit of matrices of all sizes over arbitrary fields
Let $M_n$ denote the $n$ by $n$ matrices.
Consider the homomorphisms
$$\phi_{n,kn}: M_n \rightarrow M_{kn}$$
which takes a matrix $A \in M_n$ to $A \otimes I_k \in M_{kn}.$
This gives a sensible way ...
- 1,429
4
votes
0
answers
172
views
reference for direct finiteness of the ring of affiliated operators
Let $\Gamma$ be a group, $N(\Gamma)$ its group von Neumann algebra,
$\newcommand{\cUG}{{\mathcal U}(\Gamma)}$
and $\cUG$ the ring of all densely-defined, closed operators $\ell^2(\Gamma)\to\ell^2(\...
- 25.8k
3
votes
0
answers
183
views
Is the construction of ring C*-algebra functorial?
Cunz and Li defined defined C*-algebras for arbitrary rings with of course some condition. One can look at their article (http://arxiv.org/abs/0905.4861). My question: is the construction functorial? ...
- 95
0
votes
0
answers
194
views
What methods have been used to study AW*-algebras up to now?
I am interested mainly in ring theory and homological algebra. Now I want to know about the research methods of AW*-algebras. So I want to know the answer to the question:"what methods have been used ...
- 1
4
votes
2
answers
499
views
rank of fin gen projective modules over C* algebras
Apologies - a better explanation than I started with - thanks to people for helping. It is obvious that there are many bad cases for rank - the problem is are there a reasonable number of good cases?
...
- 1,143
5
votes
1
answer
254
views
Well defined Tensoring of spectral triples
Hi,
I have a misunderstanding that I am hoping is really quite trivial. I will give my question directly and context below for those that need/want it.
Question: In connes standard model he takes ...
- 133
2
votes
1
answer
438
views
Reference request (or otherwise): Adjoint action
I am interested in clearing up a confusion of mine. I will try to make my question as clear as I can but I apologize in advance if this is not the case.
Given a unitary group of some unital ...
- 133
1
vote
0
answers
140
views
Diagonalizing matrices of linear forms of indeterminates
Let $B$ be a matrix with elements as linear forms of indeterminates. Is there a proper diagonalization procedure for such matrices like those of matrices with real and complex entries?
- 13.9k
40
votes
9
answers
10k
views
Simplest examples of rings that are not isomorphic to their opposites
What are the simplest examples of
rings that are not isomorphic to their
opposite rings? Is there a science to constructing them?
The only simple example known to me:
In Jacobson's Basic Algebra (...
- 5,654
12
votes
5
answers
2k
views
Group ring and left zero divisor
Let $K$ be a finite field and $G$ be a discrete group.
Is it true that for every $a,b\in K[G]$ the condition $ab=0$ implies $ba=0$?
It does not seem to be related to zero divisor problem, any ...
- 4,705
2
votes
2
answers
207
views
Are all automorphisms of Lin(V) given by similarity transforms?
Let $V$ be a vector space with dimension greater than 1 over the field $F$ and $Sim = \{(f\in \operatorname{Lin}(V))\mapsto gf(g^{-1}) : g\in \operatorname{GL}(V)\}$, ie $Sim$ is the set of all ...
user5810
17
votes
1
answer
710
views
Standard polynomials applied to matrices
The standard polynomial in $r$ non-commuting indeterminates $x_1,\ldots,x_r$ is defined by
$${\mathcal S}_r(x_1,\ldots,x_r):=\sum_{\sigma\in S_r}\epsilon(\sigma)x_{\sigma(1)}x_{\sigma(2)}\cdots x_{\...
- 52.3k
6
votes
2
answers
1k
views
Are the banded versions of a positive definite matrix positive definite?
Consider $M$, a positive definite matrix. Let $M^{(1)}$ be the diagonal matrix which agrees with $M$ on the diagonal ($M_{ii}=M^{(1)}_{ii}$). We have that $M^{(1)}$ is positive definite because it is ...
- 375
26
votes
7
answers
5k
views
Commutative subalgebras of M_n
For a given $n$, is there any characterization for the commutative subalgebras of $M_n(\Bbb{C})$? I would like to know how many commutative subalgebras there are for each possible dimension.
In view ...
- 397
1
vote
1
answer
433
views
Intersection of ideals in C*-algebra or even rings in general
Dear all,
here is a question that has been bothering me. It goes without saying that I would appreciate any help in answering it.
Let {I_k} be a countable sequence of two sided closed ideals in a C*-...
