added to *KK-theory* brief remark and reference to relation to stable $\infty$-categories / triangulated categories

brief note on *continuous field of C*-algebras*

brief definition: *positive operator*

expanded the section *Idea – In brief* at *Bohr topos* just a little bit, in order to amplify the relation to Jordan algebras better (which previously was a bit hidden in entry).

I have edited a bit at *Fredholm operator*. Also started a stubby *Fredholm module* in the process. But it remains very much unfinished. Have to interrupt now for a bit.

I finally gave the *Connes-Lott-Chamseddine-Barrett model* its own entry. So far it contains just a minimum of an Idea-section and a minimum of references.

This was prompted by an exposition on *PhysicsForums Insights* that I wrote: *Spectral standard model and String compactifications*

I have been touching and editing a bit more the circle of entries on the foundations of quantum mechanics which all revolve around the phenomenon that the space of states in quantum mechanics is all determined (just) by the Jordan algebra structure on the algebra of observables, and notably by the poset of commutative subalgebras of the algebra of observables:

The last of these entries is new, but essentially just split-off from “poset of commutative subalgebras” for the moment. The other entries in the list I have mildly edited, mainly cross-linking them with each other. At *Kochen-Specker theorem* I did a bit more editing, but mainly just trying to prettify the formatting and the layout of the paragraphs and cross-links..

I wanted to do more, but I am running of out time now.

Anyway, I think together these theorems paint a picture that is noteworthy and hasn’t been highlighted much. The proponents of looking at QM through the ringed topos over os poset of commutative subalgebras highlight Kochen-Specker, but I find Gleason’s theorem is actually a *stronger* argument for this approach, while Kochen-Specker is then more of a nice spin-off. Also Alfsen-Shultz combined with Harding-Döring-Hamhalter is essentially a re-formulation of Gleason that amplifies more the poset structure on the poset of commutative subalgebras.

Here Gleason and, via Jordan, Alfsen-Shultz of course go back to the very roots of QM in the 1950s, whereas Döring et al is recent. This is maybe noteworthy.

More later. Have to run now.

]]>(brushed up the definition, added four basic classes of examples)

]]>created *Baum-Connes conjecture* with an emphasis on the *Green-Julg theorem* (of the statement in KK-theory).

I have started one of those hyperlinked indices at he “reference”-entry *K-Theory for Operator Algebras*.

I just noticed that *Gelfand-Naimark theorem* (together with a dozen of variants of spelling) used to be redirecting to *Gelfand spectrum*, which however had and has nothing to say about it. As a quick fix, I gave it its own entry now, with an absolute minimum of content. Needs expanding now. I also edited the pointers to this from the Properties-section at *C*-algebra*.

added to the list of References at *poset of commutative subalgebras* the following article

- Jan Hamhalter,
*Isomorphisms of ordered structures of abelian $C^\ast$-subalgebras of $C^\ast$-algebras*, J. Math. Anal. Appl. 383 (2011) 391–399 (journal)

kindly pointed out to me by Andreas Döring. This generalizes Döring’s result already discussed there from von Neumann algebras to more general $C^\ast$-algebras.

]]>created a minimum at *Kadison-Singer problem*

brief entry for *amplimorphism*

I added a reference to C-star-system. I propose that we change the name of the page to the C-star dynamical system; this is the standard full term, jargon which is skipping dynamical is confusing for an outsider and not explicative. I can imagine many other things which deserve that name.

]]>Circumstances prompted me to write a kind of pamphlete pointing out some aspects that seem worth taking notice of have not found much appreciation yet:

This surveys how basic theorems about the standard foundation of quantum mechanics imply an accurate geometric incarnation of the “phase space in quantum mechanics” by an order-theoretic structure that combines with an algebraic structure to a ringed topos, the “Bohr topos”. While the notion of Bohr topos has been *motivated* by the Kochen-Specker theorem, the point here is to highlight that taking into account further theorems about the standard foundations of quantum mechanics, the notion effectively follows automatically and provides an accurate and useful description of the geometry of “quantum phase space” also in quantum field theory.

brief entry “daseinisation”

(Note: I am not embracing the term, I just happen to want to record that somebody proposed it.)

]]>brief entry for *spectral presheaf*

created *bootstrap category*

I am starting an entry *Poincaré duality algebra*, but it still needs some attention

created *unitisation of C*-algebras*

started a stub *equivariant KK-theory* with some quick notes. But still very stubby.