# neverendingbooks

• ## tweedledee and tweedledum

Tweedledum is a first-generation iMac (233 MHz slot-loading, 192Mb RAM, No Airport) whereas Tweedledee is 2nd-generation (350 MHz front-loading, 192Mb RAM, Airport card). A couple of weeks ago I replaced their original hard-discs (4 Gb resp. 6 Gb) by fat 120 Gb discs and from this weekend they serve as our backup-facility. Tweedledee is connected […]

• ## noncommutative geometry

Today I did prepare my lectures for tomorrow for the NOG master-class on non-commutative geometry. I\’m still doubting whether it is worth TeXing my handwritten notes. Anyway, here is what I will cover tomorrow : – Examples of l-algebras (btw. l is an arbitrary field) : matrix-algebras, group-algebras lG of finite groups, polynomial algebras, free…

• ## Van Eck phreaking

This week I reread with pleasure all 918 pages of Cryptonomicon by Neal Stephenson and found out that last time I had been extremely choosy in subplots. There are 4 major plots : one contemporary (a couple of geeks trying to set up a data-haven) and three WW2 stories : the Waterhouse-plot about cracking Enigma…

• ## a noncommutative Grothendieck topology

We have seen that a non-commutative $l$-point is an algebra$P=S_1 \\oplus … \\oplus S_k$with each $S_i$ a simple finite dimensional $l$-algebra with center $L_i$ which is a separable extension of $l$. The centers of these non-commutative points (that is the algebras $L_1 \\oplus … \\oplus L_k$) are the open sets of a Grothendieck-topology on $l$.…

• ## Fox & Geese

The game of Fox and Geese is usually played on a cross-like board. I learned about it from the second volume of the first edition of Winning Ways for your Mathematical Plays which is now reprinted as number 3 of the series. In the first edition, Elwyn Berlekamp, John Conway and Richard Guy claimed that…

• ## SNORTgo

The game of SNORT was invented by Simon Norton. The rules of its SNORTgo-version are : black and white take turns in putting a stone on a go-board such that no two stones of different colour occupy neighbouring spots. In contrast to COLgo it is a hot game meaning that many of its positions are…

• ## Galois and the Brauer group

Last time we have seen that in order to classify all non-commutative $l$-points one needs to control the finite dimensional simple algebras having as their center a finite dimensional field-extension of $l$. We have seen that the equivalence classes of simple algebras with the same center $L$ form an Abelian group, the Brauer group. The…

• ## iHome phase 2 ended

More than a month ago I started a long term project trying to make the best of our little home network. The first couple of weeks I managed to get iTunes, iPhoto and iMovie-files flowing from any computer to the living room (the TV-set for photo and mpeg-files and squeezebox for audio files). The last…

• ## connected component coalgebra

Never thought that I would ever consider Galois descent of semigroup coalgebras but in preparing for my talks for the master-class it came about naturally. Let A be a formally smooth algebra (sometimes called a quasi-free algebra, I prefer the terminology noncommutative curve) over an arbitrary base-field k. What, if anything, can be said about…

• ## Brauer’s forgotten group

Non-commutative geometry seems pretty trivial compared to commutative geometry : there are just two types of manifolds, points and curves. However, nobody knows how to start classifying these non-commutative curves. I do have a conjecture that any non-commutative curve can (up to non-commutative birationality) be constructed from hereditary orders over commutative curves by universal methods…