http://www.neverendingbooks.org/index.php/a-for-aggregates.html lieven le bruyn's blog Fri, 20 Jan 2012 16:50:41 +0100 hourly 1 http://wordpress.org/?v=3.3.1 http://www.neverendingbooks.org/index.php/a-for-aggregates.html/comment-page-1#comment-10019 down with determinants | neverendingbooks Sat, 11 Dec 2010 12:20:13 +0000 http://www.neverendingbooks.org/?p=318#comment-10019 [...] I cannot resist mentioning a trivial observation I made last week when thinking once again about THE rationality problem and which may be well known to others. Recall from the previous post that rationality of the [...] [...] I cannot resist mentioning a trivial observation I made last week when thinking once again about THE rationality problem and which may be well known to others. Recall from the previous post that rationality of the [...]

]]> http://www.neverendingbooks.org/index.php/a-for-aggregates.html/comment-page-1#comment-4207 B for bricks | neverendingbooks Sat, 12 Jan 2008 15:15:13 +0000 http://www.neverendingbooks.org/?p=318#comment-4207 <p>[...] Last time we argued that a noncommutative variety might be an aggregate which locally is of the form $wis{rep}~A$ for some affine (possibly non-commutative) $C$-algebra $A$. However, we didn't specify what we meant by 'locally' as we didn't define a topology on $wis{rep}~A$, let alone on an arbitrary aggregate. Today we will start the construction of a truly non-commutative topology on $wis{rep}~A$. Here is the basic idea : we start with a thick subset of finite dimensional representations on which we have a natural (ordinary) topology and then we extend this to a non-commutativce topology on the whole of $wis{rep}~A$ using extensions. The impatient can have a look at my old note A noncommutative topology on rep A but note that we will modify the construction here in two essential ways. In that note we took $wis{simp}~A$, the set of all fnite dimensional simple representations, as thick subset equipped with the induced Zariski topology on the prime spectrum $wis{spec}~A$. However, this topology doesn't behave well with respect to the gluings we have in mind so we will extend $wis{simp}~A$ substantially. Sphere: Related Content [...]</p> [...] Last time we argued that a noncommutative variety might be an aggregate which locally is of the form $wis{rep}~A$ for some affine (possibly non-commutative) $C$-algebra $A$. However, we didn't specify what we meant by 'locally' as we didn't define a topology on $wis{rep}~A$, let alone on an arbitrary aggregate. Today we will start the construction of a truly non-commutative topology on $wis{rep}~A$. Here is the basic idea : we start with a thick subset of finite dimensional representations on which we have a natural (ordinary) topology and then we extend this to a non-commutativce topology on the whole of $wis{rep}~A$ using extensions. The impatient can have a look at my old note A noncommutative topology on rep A but note that we will modify the construction here in two essential ways. In that note we took $wis{simp}~A$, the set of all fnite dimensional simple representations, as thick subset equipped with the induced Zariski topology on the prime spectrum $wis{spec}~A$. However, this topology doesn't behave well with respect to the gluings we have in mind so we will extend $wis{simp}~A$ substantially. Sphere: Related Content [...]

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