Abelianizing Vertex Algebras
By Haisheng Li. 2004
81 citations recorded by the source corpus.
To every vertex algebra V we associate a canonical decreasing sequence of subspaces and prove that the associated graded vector space gr(V) is naturally a vertex Poisson algebra, in particular a commutative vertex algebra. We establish a relation between this decreasing sequence and the sequence Cn introduced by Zhu. By using the (classical) algebra gr(V), we prove that for any vertex algebra V, C2-cofiniteness implies Cn-cofiniteness for all n≥2. We further use gr(V) to study generating subspaces of certain types for lower truncated ℤ-graded vertex algebras.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/66e180a09f3f37b7e2833d751ac0a42aef7daffe
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In Algebra and Number Theory
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Citations in the corpus
- Quasi-finite algebras graded by Hamiltonian and vertex operator algebras (2005, unknown): “ the maximum. – 37 – Note 8.3.2 The argument described above is a refined variation of the proof of Theorem 3.2.7 in [NaT]. The idea of utilizing the relation (8.3.5) goes back to [GaN]. See [Buh] and [Li2] for related results. We will say that a compatible degreewise complete Poisson algebra is quas”
- Associated Varieties of Modules Over Kac–Moody Algebras and C2-Cofiniteness of W-Algebras (2010, methodology): “ΓpM d = 0 for p≫ 0, where ΓpM d = Md∩ΓpM. The associated graded space grF M= L FpM/Fp+1M is naturally a graded module over the graded vertex Poisson algebra grF V. We denote by {FpM} the Li filtration [Li2] of a V-module M, which is a compatible filtration. We have F0M/F1M = M/C2(M), where C2(M) is th”
- A remark on the C2-cofiniteness condition on vertex algebras (2010, background): “Then {F p M} is a compatible filtration [24].”