2
votes
0answers
125 views

C*-algebras and bounded relations

I'm trying to get used to the language of generators and relations for C*-algebras through Loring's "Lifting Solutions to Perturbing Problems in C*-Algebras". So far this is what I got from the first ...
5
votes
1answer
231 views

A generalized K- theory via generalized idempotents

Edit After the answer by Neil Strickland, I add the word "a ring" in this new version. In the literature, there is a concept of generalized idempotent: an n- idempotent is an element $a$ of a Banach ...
7
votes
1answer
164 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 ...
3
votes
1answer
251 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 ...
3
votes
0answers
108 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 ...
3
votes
0answers
157 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? ...
0
votes
0answers
180 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 ...
4
votes
2answers
398 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? ...
4
votes
1answer
189 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 ...
2
votes
1answer
253 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 ...
1
vote
0answers
127 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?
17
votes
8answers
3k 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 ...
10
votes
3answers
981 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 ...
2
votes
2answers
200 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 ...
15
votes
1answer
560 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 ...
4
votes
2answers
424 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 ...
10
votes
7answers
1k 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 ...
1
vote
1answer
349 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 ...