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SUMMARY:Chain conditions in the enveloping algebra of the Witt algebra - S
 usan Sierra (Edinburgh)
DTSTART:20181024T153000Z
DTEND:20181024T163000Z
UID:TALK111784@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:Let W be the positive Witt algebra\, which consists of element
 s of\nthe form f(x)(d/dx) for some polynomial f(x) with complex coefficien
 ts.  The universal enveloping algebra U(W) is a\ncomplicated and interest
 ing ring\, which was only shown not to be noetherian\nin 2013.\n\nWe study
  the two-sided ideal structure of U(W).  In contrast to one-sided\nideals
 \, the two-sided structure appears to be relatively sparse\; in fact we\nc
 onjecture that U(W) has ACC on two-sided ideals and that any proper factor
 \nring of U(W) has finite Gelfand-Kirillov dimension.  We present evidenc
 e\ntowards these conjectures.  Our main technique is to study the Poisson
 \nstructure of the associated graded ring of U(W).\n\nThis is joint work w
 ith Alexey Petukhov and Natalia Iyudu.\n
LOCATION:MR12
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