Chain conditions in the enveloping algebra of the Witt algebra

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• Susan Sierra (Edinburgh)
• Wednesday 24 October 2018, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Christopher Brookes.

Let W be the positive Witt algebra, which consists of elements of the form f(x)(d/dx) for some polynomial f(x) with complex coefficients.  The universal enveloping algebra U(W) is a complicated and interesting ring, which was only shown not to be noetherian in 2013.

We study the two-sided ideal structure of U(W).  In contrast to one-sided ideals, the two-sided structure appears to be relatively sparse; in fact we conjecture that U(W) has ACC on two-sided ideals and that any proper factor ring of U(W) has finite Gelfand-Kirillov dimension.  We present evidence towards these conjectures.  Our main technique is to study the Poisson structure of the associated graded ring of U(W).

This is joint work with Alexey Petukhov and Natalia Iyudu.

This talk is part of the Algebra and Representation Theory Seminar series.

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