2007/10/31 by Andrew R. Linshaw · 20 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Centralizer and normalizer #Discrete mathematics #Graph #Invariant (physics) #Lie algebra #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Subalgebra #Universal enveloping algebra #Vertex (graph theory) #math.QA #math.RT
paper · pdf · doi:10.1016/j.jpaa.2008.08.006
published in Journal of Pure and Applied Algebra 213(5), 632-648 (Elsevier BV) · a few typos corrected, final version
arxiv created 2008/09/08 · openalex publication_date 2008/09/20 · openalex created_date 2016/06/24 · arxiv updated 2020/08/10 · openalex updated_date 2026/08/05
Attached to a vector space V is a vertex algebra S(V) known as the beta-gamma system or algebra of chiral differential operators on V. It is analogous to the Weyl algebra D(V), and is related to D(V) via the Zhu functor. If G is a connected Lie group with Lie algebra g, and V is a linear G-representation, there is an action of the corresponding affine algebra on S(V). The invariant space S(V)g[t] is a commutant subalgebra of S(V), and plays the role of the classical invariant ring D(V)G. When G is an abelian Lie group acting diagonally on V, we find a finite set of generators for S(V)g[t], and show that S(V)g[t] is a simple vertex algebra and a member of a Howe pair. The Zamolodchikov W3 algebra with c=-2 plays a fundamental role in the structure of S(V)g[t].