Susan Sierra, University of Edinburgh
“The universal enveloping algebra of the Virasoro algebra is not noetherian.”
The Virasoro algebra is an infinite-dimensional Lie algebra of great importance in physics and representation theory. We answer a long-standing question and show that its universal enveloping algebra is not noetherian. We do so by exhibiting a homomorphism from the positive part of the enveloping algebra to a polynomial ring over the Weyl algebra, and analysing the image.
This is joint work with Chelsea Walton.