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Topic: The Weyl Algebra - Why is it not semisimple
Replies: 2   Last Post: Mar 25, 2008 12:19 PM

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Rupert

Posts: 7
Registered: 12/14/06
The Weyl Algebra - Why is it not semisimple
Posted: Mar 25, 2008 7:52 AM
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Hi,

Going through some lecture notes for a rings and modules course and
I've got a bit stuck on the result that the (first) Weyl Algebra, W,
generated by x,D with Dx-xD=1 is not semisimple.

In my lecture notes the lecturer proved W has no finite dimensional
representation (using traces of matrices), and by process of
elimination I presume that this is meant to imply W is not semisimple.
I notice (googling frantically) that "Infinite Length Modules", by
Henning Krause, Claus Michael Ringel on page 131states the same result
in what appears to be the same context, but I can't for the life of me
work out why it helps!

Can anyone explain please?

Thanks,

Rupert



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