Vertex algebras and vertex Poisson algebras

Details Vertex algebras and vertex Poisson algebras Vertex algebras and vertex Poisson algebras

2002-09-23

arxiv.org/abs/math/0209310v2

Mathematics

Quantum Algebra

Some typos and errors are fixed and some results of Section 4 are reformulated. This is the final version to appear in Commun.

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Vertex algebras and vertex Poisson algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Vertex algebras and vertex Poisson algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Vertex algebras and vertex Poisson algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-577042