Vertex algebras and vertex Poisson algebras
By Haisheng Li. 2002
109 citations recorded by the source corpus.
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=∐n∈ℕV(n) with , 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/05672bd986ad38c88779bd8704375ebed1c4aa64
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Citations in the corpus
- Representation theory of W-algebras (2005, unknown): “ned on grF V. Therefore, they define on grF V a vertex algebra structure. The vertex algebra grF V is called the graded vertex algebra associated with the filtered vertex algebra V. Remark A.6.2. H. Li [43] defined the notion of filtered vertex algebras for a different propose. A.7. Filtered Universal En”
- Associated Varieties of Modules Over Kac–Moody Algebras and C2-Cofiniteness of W-Algebras (2010, methodology): “Here a(n) with n≥ 0 is the coefficient of z−n−1 in the field Y−(a,z) in the notation of [FBZ, 16.2]. Throughout the paper by a R∞-module Mwe mean a module over the vertex Poisson algebra in the sense of [Li1] unless otherwise stated. In particular Mis equipped with the action of a(n) with a∈ R∞, n≥ 0, ”
- A remark on the C2-cofiniteness condition on vertex algebras (2010, background): “= , G Let L 2 In [Li04] it is assumed that V is Z ≥ 0 -graded and V 0 = C , but this condition can be easily relaxed, as we can see from Proposition 2.6.1.”
- Simple current extensions beyond semi-simplicity (2015, background): “n) as a deformation of the classical invariant ring R= (Sym L k≥0 Vk) O(n), where V k ∼= Cn as O(n)-modules. In particular, H(n) admits an O(n)- invariant good increasing filtration in the sense of Li [Li2], and gr(H(n)O(n)) ∼= Ras differential graded commutative rings. Using Weyl’s first fundamental ”
- Abelianizing Vertex Algebras (2004, background): “Furthermore, the following construction of good increasing filtrations was also given in [ Li2 ]:”