Comments on: Bost-Connes for ringtheorists http://www.neverendingbooks.org/index.php/bost-connes-for-ringtheorists.html lieven le bruyn's blog Wed, 28 Jul 2010 16:42:15 +0200 hourly 1 http://wordpress.org/?v=3.0 By: BC stands for Bi-Crystalline graded | neverendingbooks http://www.neverendingbooks.org/index.php/bost-connes-for-ringtheorists.html/comment-page-1#comment-4635 BC stands for Bi-Crystalline graded | neverendingbooks Sat, 26 Jan 2008 16:26:45 +0000 http://www.neverendingbooks.org/index.php/bost-connes-for-ringtheorists.html#comment-4635 <p>[...] geometry and the Riemann zeta functionthe Bost-Connes coset spacethe Bost-Connes Hecke algebraBost-Connes for ringtheoristsBC stands for Bi-Crystalline [...]</p> [...] geometry and the Riemann zeta functionthe Bost-Connes coset spacethe Bost-Connes Hecke algebraBost-Connes for ringtheoristsBC stands for Bi-Crystalline [...]

]]> By: lieven http://www.neverendingbooks.org/index.php/bost-connes-for-ringtheorists.html/comment-page-1#comment-4563 lieven Thu, 24 Jan 2008 13:37:00 +0000 http://www.neverendingbooks.org/index.php/bost-connes-for-ringtheorists.html#comment-4563 <p>@javier, a few hours later im a bit embarrassed about this post. i was indeed trying too hard to fit it into something like a strongly graded setting but i forgot one important fact : algebras such as Q[Q/Z] have lots of idempotents and once you bring them into play all this epi/mono nonsense of the post because much more transparant. i guess thats what happens when you want to view C^*-type algebras (or at least von neumann regular algebras) too much from a Noetherian skew polynomial/quantum algebra perspective. i hope to clarify things soon.</p> @javier, a few hours later im a bit embarrassed about this post. i was indeed trying too hard to fit it into something like a strongly graded setting but i forgot one important fact : algebras such as Q[Q/Z] have lots of idempotents and once you bring them into play all this epi/mono nonsense of the post because much more transparant. i guess thats what happens when you want to view C^*-type algebras (or at least von neumann regular algebras) too much from a Noetherian skew polynomial/quantum algebra perspective. i hope to clarify things soon.

]]> By: javier http://www.neverendingbooks.org/index.php/bost-connes-for-ringtheorists.html/comment-page-1#comment-4562 javier Thu, 24 Jan 2008 13:20:46 +0000 http://www.neverendingbooks.org/index.php/bost-connes-for-ringtheorists.html#comment-4562 <p>Cannot be considered an expert ringtheorist, nor have any proper references around here right now, so please take this just as some wishful thinking.</p> <p>The algebra looks crazily big to fit inside most of the "classical type" constructions in ring theory, so my guess is that the right kind of construction that could bear some light over it would rather be related with some quantum group stuff.</p> <p>Concretely (and again, please take this with your gloves on) since most of your defining relations look like (twisted) commutators and involve mainly quadratic relations, they look pretty much like the relations defining some Yangians.</p> <p>There used to be some lecture notes by Maxim Nazarov in the website of the first GAMAP, but apparently the page is not there anymore, and I left my notes back home...</p> Cannot be considered an expert ringtheorist, nor have any proper references around here right now, so please take this just as some wishful thinking.

The algebra looks crazily big to fit inside most of the “classical type” constructions in ring theory, so my guess is that the right kind of construction that could bear some light over it would rather be related with some quantum group stuff.

Concretely (and again, please take this with your gloves on) since most of your defining relations look like (twisted) commutators and involve mainly quadratic relations, they look pretty much like the relations defining some Yangians.

There used to be some lecture notes by Maxim Nazarov in the website of the first GAMAP, but apparently the page is not there anymore, and I left my notes back home…

]]> By: History of Mathematics Blog » Blog Archive » Bost-Connes for ringtheorists http://www.neverendingbooks.org/index.php/bost-connes-for-ringtheorists.html/comment-page-1#comment-4529 History of Mathematics Blog » Blog Archive » Bost-Connes for ringtheorists Wed, 23 Jan 2008 16:03:17 +0000 http://www.neverendingbooks.org/index.php/bost-connes-for-ringtheorists.html#comment-4529 <p>[...] unknown: [...]</p> [...] unknown: [...]

]]> By: EquMath: Math Lessons » Blog Archive » Bost-Connes for ringtheorists http://www.neverendingbooks.org/index.php/bost-connes-for-ringtheorists.html/comment-page-1#comment-4528 EquMath: Math Lessons » Blog Archive » Bost-Connes for ringtheorists Wed, 23 Jan 2008 15:58:22 +0000 http://www.neverendingbooks.org/index.php/bost-connes-for-ringtheorists.html#comment-4528 <p>[...] admin: [...]</p> [...] admin: [...]

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