The spectral-triples tag has no usage guidance.

**1**

vote

**0**answers

106 views

### Is there a non-integer in the dimension spectrum for the Heisenberg group?

Let $\Gamma = \langle a,b,c \ | \ c=aba^{-1}b^{-1}, \ ac=ca, \ bc = cb \rangle$ be the discrete Heisenberg group.
Let $\ell: \Gamma \to \mathbb{N} $ be the word length on $\Gamma$. This group has a ...

**12**

votes

**0**answers

592 views

### Can we define spectral triples using the language of rigged Hilbert spaces?

The traditional mathematical approach to quantum mechanics,
as developed by von Neumann, is based on Hilbert spaces and unbounded self-adjoint operators.
Another approach, which more closely resembles ...

**3**

votes

**1**answer

252 views

### Manifolds whose isometry group is Pati-Salam?

By the Pati-Salam group I refer to SU(2) x SU(2) x SU(4). It can be obtained as the group of isometries of the 8 dimensional manifold $S^3 \times S^5$, but I wonder if this is the only 8 dimensional ...

**18**

votes

**3**answers

2k views

### Noncommutative smooth manifolds

Connes defined a noncommutative analog of a closed oriented Riemannian spin^c manifold using spectral triples.
Using his definition it is unclear how to separate the smooth structure from the metric.
...

**4**

votes

**0**answers

244 views

### Obstructions to existence of finitely summable spectral triples

Connes proved in his beautiful paper "Compact metric spaces, Fredholm modules, and hyperfiniteness" published in 1989 that if $(A,H,D)$ is a finitely summable spectral triple with a unital $C^*$-...

**12**

votes

**5**answers

2k views

### Non-commutative geometry from von Neumann algebras?

The Gelfand transform gives an equivalence of categories from the category of unital, commutative $C^*$-algebras with unital $*$-homomorphisms to the category of compact Hausdorff spaces with ...