### Seminar in Algebra, Lie Theory, and Geometry

# Alexey Petukhov

### (IPPI Moscow)

## "Ideals in the enveloping algebra of the positive Witt algebra"

** Date: ** |
Thu, April 26, 2018 |

** Time: ** |
13:30 |

** Place: ** |
Seminar Room (120), Research I |

**Abstract:** Let W be a Lie algebra algebra with a C-basis {en:n?Z?1} and Lie bracket [ei,ej]=(j?i)ei+j (Witt algebra). In our joint work with S. Sierra we study the two-sided ideal structure of the universal enveloping algebra U(W) of W. We show that if I is a (two-sided) ideal of U(W) is generated by quadratic expressions in the ei, then U(W)/I has finite Gelfand-Kirillov dimension, and that such ideals satisfy the ascending chain condition. We conjecture that analogous facts hold for arbitrary ideals of U(W), and verify a version of these conjectures for radical Poisson ideals of the symmetric algebra S(W+).