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There is an alternative proof for FTA using "Fredholm operators on Hilbert spaces": Assume that $P(z)=z^n+a_{n-1}z^{n-1}+\ldots+a_1 z+a_0$ has no root in $\mathbb{C}$. Then for every $\epsilon$ the …

A $C^{*}$ algebra $A$ is graded by $\mathbb{Z}_{n}$ iff it can be acted by $\mathbb{Z}_{n}$. So we associate the $C^{*}$ algebra $A\rtimes \mathbb{Z}_{n}$ to a $\mathbb{Z}_{n}$-graded $C^{*}$ alg …

To what extent, the following types of Lie algebras are classified : Those Lie algebras $L$ such that every Lie Group $G$ with $Li(G)\sim L$, is necessarily compact.

One can consider an alternative concept of prime matrix as follows: A matrix $A\in M_n(\mathbb{Z})$ is prime if for any factorization $A=BC$ we have either $Det(B)\in \{-1,1\}$ or $Det(C)\in \{-1,1 …

I think that there is a metric on the huge space of all $C^{*}$ algebras. What is the explicit definition of this metric?may you introduce me a reference? Moreover is the restriction of this metr …

Let $G$ be a locally compact group. Put $I(G)=\ker: C^{*}(G) \to C_{r}^{*} (G)$, the kernel of the canonical morphism. What type of $C^{*}$ algebras can not be isomorphic to $I(G)$, for some loca …

A linear $1$-form on $\mathbb{R}^n$ is a $1$-form $\alpha=\sum_i P_i(x_1,x_2,\ldots,x_n)dx_i$ such that each $P_i$ is in the linear form $P_i=\sum_j a_{ij}x_j$. A linear foliation of $\mathbb{R}^n \ …

Many years ago I found in google the notation "Holomorph of group". It is the semi direct product of $G$ with $Aut(G)$. Why is the term "Holomorph" used here, while it is usually used for complex anal …

What are some papers or talks on the philosophy of mathematics which contains some statements about the unnecessary and unreasonable application of mathematics in other areas of science? I found …

Let $X$ be a compact Hausdorff topological space put $A=C(X)$ the $C^*$ algebra of all complex valued continuous functions. The Gelfand correspondence between the category of compact …

What papers or references have been devoted for a noncommutativization of "Fixed point theory". Here the terminology Noncommutativiztion, as usual, indicates to that famous table with 2 columns: f …

In the literature, is there a non-commutative analogue of the fact that every Riemannian manifold whose isometry group has sharp dimension must be a constant curvature manifold?

You wrote "I believe that orbits space coming from real-analytic foliations should have a "nicer" structure". I think that this nicer structure arises when we consider a more technical "Leaf space" s …

For a self map $f$ on a topological space $X$ we replace "trace" with "determinant" in the alternative Lefschetz formula $$\Lambda(f)=\sum(-1)^i trace(f^*)|H^i(X,\mathbb{Q})$$ So we have $$\Lam …

What type of obstructions have been studied so that the unit tangent bundle of a Riemannian 2-(4-)manifold have a structure of a principal $S^{1}$-($S^{3}$-)bundle?