Yuly Billig
Carleton University, Ottawa, Canada
Representations of the Determinant Lie algebra.
Abstract: The Determinant Lie algebra is a Lie algebra with a basis {E(u) | u \in Z^2} with Lie bracket [E(u), E(v)] = det(u,v) E(u+v). It admits a 2-dimensional central extension. We study representation theory of the central extension of this Lie algebra, and construct irreducible modules with finite-dimensional weight spaces. In order to construct such modules we introduce the concept of a jet Lie algebra. Given a Lie algebra with a polynomial structure constants, we associate to it another Lie algebra, which we call the jet Lie algebra. One of the modules we construct admits the structure of a vertex operator algebra. This is a joint work with Kenji Iohara and Olivier Mathieu.