Book Review: Vertex algebras and algebraic curves

Vertex Algebras and Algebraic Curves

Cherednik Algebras for Algebraic Curves

For any algebraic curve C and n ≥ 1, P. Etingof introduced a ‘global’ Cherednik algebra as a natural deformation of the cross product D(Cn)⋊Sn, of the algebra of differential operators on Cn and the symmetric group. We provide a construction of the global Cherednik algebra in terms of quantum Hamiltonian reduction. We study a category of character Dmodules on a representation scheme associated ...

Vertex Lie algebras, vertex Poisson algebras and vertex algebras

The notions of vertex Lie algebra and vertex Poisson algebra are presented and connections among vertex Lie algebras, vertex Poisson algebras and vertex algebras are discussed.

Vertex algebras and vertex poisson algebras

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 i...

Tree Algebras: an Algebraic Axiomatization of Intertwining Vertex Operators

We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a tree algebra. Using the Riemann-Hilbert correspondence, we further prove that a vertex tensor category in the sense of Huang and Lepowsky gives rise to a tree algebra over C. We also show that the chiral WZW model of a simply c...