Timeline for Proof a Weyl Algebra isn't isomorphic to a matrix ring over a division ring
Current License: CC BY-SA 3.0
6 events
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| Jul 7, 2013 at 18:25 | history | edited | Alicia Garcia-Raboso | CC BY-SA 3.0 |
MathJax
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| Jun 26, 2011 at 17:03 | comment | added | Mariano Suárez-Álvarez | ...and, moreover, the division rings in questions need not be finite dimensional algebras over the basefield of $A_n$. | |
| Nov 9, 2009 at 23:13 | comment | added | Qiaochu Yuan | The question is about matrix rings over division rings, not over fields. Unless you're just stating a weaker result? | |
| Nov 9, 2009 at 16:05 | comment | added | David Jordan | Which ring are you calling underlying? The base field? This is part of the standard proof that W_n is simple. In fact not only can it not have finite dimensional representations, but it's smallest representations have so-called Gelfand Kirillov dimension n, meaning that they are infinite-dimensional, and graded, and the dimension of the kth piece is on the order of k^{n-1}. These are called holonomic modules. The prototype example is C[x_1,...x_n] with its natural action. The dimension of the kth graded part is \choose{k+n-1}{n-1}, which is approximately k^{n-1} as k-->\infty. | |
| Nov 9, 2009 at 15:01 | comment | added | Qiaochu Yuan | I was going to say this, but I wasn't sure if it still works when the underlying ring is noncommutative. | |
| Nov 9, 2009 at 14:51 | history | answered | David Jordan | CC BY-SA 2.5 |