## View abstract

### Session S16 - Quantum symmetries

Wednesday, July 14, 11:-1 ~ 11:24 UTC-3

## The Poisson spectrum of the symmetric algebra of the Virasoro algebra

### Susan Sierra

#### University of Edinburgh, UK   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak6d3a3e2f05fc9440f0bdb38c34c3be19').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy6d3a3e2f05fc9440f0bdb38c34c3be19 = 's.s&#105;&#101;rr&#97;' + '&#64;'; addy6d3a3e2f05fc9440f0bdb38c34c3be19 = addy6d3a3e2f05fc9440f0bdb38c34c3be19 + '&#101;d' + '&#46;' + '&#97;c' + '&#46;' + '&#117;k'; var addy_text6d3a3e2f05fc9440f0bdb38c34c3be19 = 's.s&#105;&#101;rr&#97;' + '&#64;' + '&#101;d' + '&#46;' + '&#97;c' + '&#46;' + '&#117;k';document.getElementById('cloak6d3a3e2f05fc9440f0bdb38c34c3be19').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy6d3a3e2f05fc9440f0bdb38c34c3be19 + '\'>'+addy_text6d3a3e2f05fc9440f0bdb38c34c3be19+'<\/a>';

Let $W$ be the Witt algebra of polynomial vector fields on the punctured complex plane, and let $Vir$ be the Virasoro algebra, the unique nontrivial central extension of $W$. We discuss joint work with Alexey Petukhov to analyse Poisson ideals of the symmetric algebra of $Vir$.

We focus on understanding Poisson primitive ideals, which can be given as the Poisson cores of maximal ideals of $\operatorname{Sym}(Vir)$ and of $\operatorname{Sym}(W)$. We give a complete classification of maximal ideals of $\operatorname{Sym}(W)$ which have nontrivial Poisson cores. We then lift this classification to $\operatorname{Sym}(Vir)$, and use it to show that if $\lambda \neq 0$, then $(z-\lambda)$ is a Poisson primitive ideal of $\operatorname{Sym}(Vir)$. We give applications to the Poisson geometry of the space of functions on $Vir$.

Joint work with Alexey Petukhov (Institute for Information Transmission Problems, Russia).