BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Sue Sierra (University of Edinburgh\, UK)
DTSTART:20250519T150000Z
DTEND:20250519T160000Z
DTSTAMP:20260423T052502Z
UID:ENAAS/123
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/123/">
 Ideals of enveloping algebras of loop algebras</a>\nby Sue Sierra (Univers
 ity of Edinburgh\, UK) as part of European Non-Associative Algebra Seminar
 \n\n\nAbstract\nLet g be a finite-dimensional simple Lie algebra\, and con
 sider the loop algebra $L_g = g[t\, t^{-1}]$ and the affine Lie algebra $\
 \hat{g}$\, which is an extension of $L_g$ by a central element $c$. We inv
 estigate two-sided ideals in the universal enveloping algebra $U(L_g)$.  I
 t is known that the rings $U(\\hat{g})/(c-\\lambda)$ are simple for any no
 nzero scalar $\\lambda$\, but the two-sided structure of $U(L_g) = U(\\hat
 {g}/(c))$ is more complicated.  We show that $U(L_g)$ does not satisfy the
  ascending chain condition on two-sided ideals\, but that the two-sided id
 eals still have a nice structure: there is a canonical collection of ideal
 s $I_n$\, parameterised by positive integers\, so that any two-sided ideal
  of $U(L_g)$ contains some $I_n$.  The ideals $I_n$ can be thought of as u
 niversal annihilators of classes of finite-dimensional representations of 
 $L_g$. This is a preliminary report on joint work with Alexey Petukhov.\n
LOCATION:https://researchseminars.org/talk/ENAAS/123/
END:VEVENT
END:VCALENDAR