# Posts Tagged: Cuntz

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## what does the monster see?

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The Monster is the largest of the 26 sporadic simple groups and has order 808 017 424 794 512 875 886 459 904 961 710 757 005 754 368 000 000 000 = 2^46 3^20 5^9 7^6 11^2 13^3 17 19 23 29 31 41 47 59 71. It is not so much the size… Read more »

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## “God given time”

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If you ever sat through a lecture by Alain Connes you will know about his insistence on the ‘canonical dynamic nature of noncommutative manifolds’. If you haven’t, he did write a blog post Heart bit 1 about it. I’ll try to explain here that there is a definite “supplément d’âme” obtained in the transition from… Read more »

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## Segal’s formal neighbourhood result

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Yesterday, Ed Segal gave a talk at the Arts. His title “Superpotential algebras from 3-fold singularities” didnt look too promising to me. And sure enough it was all there again : stringtheory, D-branes, Calabi-Yaus, superpotentials, all the pseudo-physics babble that spreads virally among the youngest generation of algebraists and geometers. Fortunately, his talk did contain… Read more »

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## coalgebras and non-geometry 2

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Last time we have seen that the _coalgebra of distributions_ of an affine smooth variety is the direct sum (over all points) of the dual to the etale local algebras which are all of the form $\mathbb{C}[[ x_1,\ldots,x_d ]]$ where $d$ is the dimension of the variety. Generalizing this to _non-commutative_ manifolds, the… Read more »

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## coalgebras and non-geometry

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In this series of posts I’ll try to make at least part of the recent [Kontsevich-Soibelman paper](http://www.arxiv.org/abs/math.RA/0606241) a bit more accessible to algebraists. In non-geometry, the algebras corresponding to *smooth affine varieties* I’ll call **qurves** (note that they are called **quasi-free algebras** by Cuntz & Quillen and **formally smooth** by Kontsevich). By definition, a qurve… Read more »

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## non-(commutative) geometry

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Now that my non-geometry post is linked via the comments in this string-coffee-table post which in turn is available through a trackback from the Kontsevich-Soibelman paper it is perhaps useful to add a few links. The little I’ve learned from reading about Connes-style non-commutative geometry is this : if you have a situation where a… Read more »

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## non-geometry

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Here’s an appeal to the few people working in Cuntz-Quillen-Kontsevich-whoever noncommutative geometry (the one where smooth affine varieties correspond to quasi-free or formally smooth algebras) : let’s rename our topic and call it non-geometry. I didn’t come up with this term, I heard in from Maxim Kontsevich in a talk he gave a couple of… Read more »

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## subscribe to my brain

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or rather, I’d like to subscribe to your brain! But I figure you’d allow this (at best) only on a ‘share-alike’ basis so let me take the first step. Maybe you already have your newsaggregator pointed to this weblog, but what if you could be able to follow all traces I leave on the web… Read more »

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## noncommutative topology (1)

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A couple of days ago Ars Mathematica had a post Cuntz on noncommutative topology pointing to a (new, for me) paper by Joachim Cuntz A couple of years ago, the Notices of the AMS featured an article on noncommutative geometry a la Connes: Quantum Spaces and Their Noncommutative Topology by Joachim Cuntz. The hallmark of… Read more »

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## From Galois to NOG

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Evariste Galois (1811-1832) must rank pretty high on the all-time list of moving last words. Galois was mortally wounded in a duel he fought with Perscheux d\’Herbinville on May 30th 1832, the reason for the duel not being clear but certainly linked to a girl called Stephanie, whose name appears several times as a marginal… Read more »

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## curvatures

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[Last time][1] we saw that the algebra $(\Omega_V~C Q,Circ)$ of relative differential forms and equipped with the Fedosov product is again the path algebra of a quiver $\tilde{Q}$ obtained by doubling up the arrows of $Q$. In our basic example the algebra map $C \tilde{Q} \rightarrow \Omega_V~C Q$ is clarified by the following picture of… Read more »

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## differential forms

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The previous post in this sequence was [(co)tangent bundles][1]. Let $A$ be a $V$-algebra where $V = C \times \ldots \times C$ is the subalgebra generated by a complete set of orthogonal idempotents in $A$ (in case $A = C Q$ is a path algebra, $V$ will be the subalgebra generated by the vertex-idempotents, see… Read more »

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## more noncommutative manifolds

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Can it be that one forgets an entire proof because the result doesn’t seem important or relevant at the time? It seems the only logical explanation for what happened last week. Raf Bocklandt asked me whether a classification was known of all group algebras l G which are noncommutative manifolds (that is, which are formally… Read more »

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## Bill Schelter’s Maxima

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Bill Schelter was a remarkable man. First, he was a top-class mathematician. If you allow yourself to be impressed, read his proof of the Artin-Procesi theorem. Bill was also among the first to take non-commutative geometry seriously. Together with Mike Artin he investigated a notion of non-commutative integral extensions and he was the first to… Read more »

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## NOG master class

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Yesterday I made reservations for lecture rooms to run the master class on non-commutative geometry sponsored by the ESF-NOG project. We have a lecture room on monday- and wednesday afternoon and friday the whole day which should be enough. I will run two courses in the program : non-commutative geometry and projects in non-commutative geometry… Read more »