Vertex algebras and vertex Poisson algebras
Abstract
This paper studies certain relations among vertex algebras, vertex Lie algebras and vertex Poisson algebras. In this paper, the notions of vertex Lie algebra (conformal algebra) and vertex Poisson algebra are revisited and certain general construction theorems of vertex Poisson algebras are given. A notion of filtered vertex algebra is formulated in terms of a notion of good filtration and it is proved that the associated graded vector space of a filtered vertex algebra is naturally a vertex Poisson algebra. For any vertex algebra $V$, a general construction and a classification of good filtrations are given. To each $\N$graded vertex algebra $V=\coprod_{n\in \N}V_{(n)}$ with $V_{(0)}=\C {\bf 1}$, a canonical (good) filtration is associated and certain results about generating subspaces of certain types of $V$ are also obtained. Furthermore, a notion of formal deformation of a vertex (Poisson) algebra is formulated and a formal deformation of vertex Poisson algebras associated with vertex Lie algebras is constructed.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2002
 DOI:
 10.48550/arXiv.math/0209310
 arXiv:
 arXiv:math/0209310
 Bibcode:
 2002math......9310L
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 Some typos and errors are fixed and some results of Section 4 are reformulated. This is the final version to appear in Commun. Contemp. Math