An algebraic analog of the Virasoro group

Abstract

The group of diffeomorphisms of a circle is not an infinite-dimensional algebraic group, though in many ways it behaves as if it were. Here we construct an algebraic model for this object, and discuss some of its representations, which appear in the Kontsevich-Witten theory of two-dimensional topological gravity through the homotopy theory of moduli spaces.

This is a version of a talk on 23 June 2001 at the Prague Conference on Quantum Groups and Integrable Systems, published in the Czechoslovak J. Physics 51 (2001)