Search Results

What is a relevant non commutative analogues for the following fact, in term of spectral triples and cyclic cohomology?: "If $M$ is a compact oriantable manifold without boundary and $X\subset M$ is …

My apology in advance if my question is elementary According to the initial definition of topological stable rank introduced by Marc Rieffel we have the following: An algebra has tsr 1 if the space …

A unital $C^*$ algebra $A$ is said a Tietze algebra if it satisfies the following: For every ideal $I$ of $A$ and every unital morphism $\phi: C[0,1] \to A/I$ there is a unital morphism $\tilde{\phi} …

What is an appropriate version of the following fact in terms of Hopf algebras and quantum groups: "For every connected Lie group $G$ the second fundamental group $\pi_2(G)$ is trivial?" Is there an …

Let $X$ be a compact Hausdorff space.Put $Vec(X)$, the space of all real (or complex) vector bundles over $X$.We put also $Vec_g(X)$, the space of all Riemannian vector bundles over $X$, that is the s …

Assume that $A$ is a complex algebra. By $C^{n}(A)$ we mean the space of all $n-$linear map $\phi:A^n \to \mathbb{C}$. An alternative $k-$ form is an element $\phi \in C^{k}(A)$ …

Let $R$ be a ring, define a topology on $AUT(R)$(Or End(R)) with the following subbase: For every two 2-sided Ideal $I$ and $J$, a subbase element is $B(I,J)=\{f\in AUT(R) \mid f(I)+J=R\}$. We can re …

Is there a terminology (and a classification) for all groupoids $G$ for which all automorphisms of $C^*_\text{red}G$ are induced from a groupoid automorphism of $G$. (A groupoid automorphism has it …

Let $H$ be a complex Hilbert space. Is there a compact Hausdorff space $X$ such that $C(X)$ is embeded in $B(H)$ and for every homeomorphism $\alpha$ of $X$ there exist a unitary operator $u\in B(H)$ …

Assume that $(G,G^0,r,s)$ is a smooth groupoid such that $G$ is a compact connected manifold. The graph of "source" and "range" maps $s, r: G \to G^0$ are compact submanifolds $S$ and $R$ of $G\times …

Let $S$ be a surface in $\mathbb{R}^3$. Inspired by the $2$-cyclic cocycle defined in page 20 of the book "Non-commutative geometry" by Alain Connes, we consider the following $3$-linear map on the s …

Let $X$ be a compact Hausdorff space and $\alpha$ be a homeomorphism of $X$. So we have a natural action of $\mathbb{Z}$ on $C(X)$ which generates the cross product algebra $C^*(X,\alpha) …

let $A$ be a $C^*$ algebra. We equip $A\otimes A$ with the spatial norm. Assume that two morphisms $a\mapsto a\otimes 1$ and $a \mapsto 1\otimes a$ are homotopic morphisms, i.e, there is a curve $ …

Is there a terminology for the following property of $C^*$ algebra $A$: For every $C^*$ algebra $B$ and surjective $C^*$ morphism $\phi: B\to A$, every normal element $y\in A$ admits a normal ele …

Let $H$ be a Hilbert space. A vector subspace $W\subset B(H)$ is called a Fredholm subspace if there is an upper bound for the absolute value of Fredholm index of all Fredholm operators $T$ in $W$. …