# Factorization of Formal Exponentials and Uniformization

@article{Barron2000FactorizationOF,
title={Factorization of Formal Exponentials and Uniformization},
author={Katrina Deane Barron and Yi-Zhi Huang and James Lepowsky},
journal={Journal of Algebra},
year={2000},
volume={228},
pages={551-579}
}
• Published 27 August 1999
• Mathematics
• Journal of Algebra
Let g be a Lie algebra over a field of characteristic zero equipped with a vector space decomposition g = g − ⊕ g + , and let s and t be commuting formal variables commuting with g. We prove that the map C: sg − [[s, t]] × tg + [[s, t]] → sg − [[s, t]] ⊕ tg + [[s, t]] defined by the Campbell–Baker–Hausdorff formula and given by esg − etg + = eC(sg − , tg + ) for g ± ∈ g ± [[s, t]] is a bijection, as is well known when g is finite-dimensional over R or C, by geometry. It follows that there exist…
14 Citations
Cardy Condition for Open-Closed Field Algebras
Let V be a vertex operator algebra satisfying certain reductivity and finiteness conditions such that $${\mathcal{C}_V}$$ , the category of V-modules, is a modular tensor category. We study
Birkhoff Type Decompositions and the Baker–Campbell–Hausdorff Recursion
• Mathematics
• 2006
We describe a unification of several apparently unrelated factorizations arising from quantum field theory, vertex operator algebras, combinatorics and numerical methods in differential equations.
Exponential Formulas and Lie Algebra Type Star Products
• Mathematics
• 2012
Given formal differential operators Fi on polynomial algebra in several variables x1;:::;xn, we discuss finding expressions Kl determined by the equation exp( P i xiFi)(exp( P j qjxj)) = exp( P l
THE MODULI SPACE OF N = 2 SUPER-RIEMANN SPHERES WITH TUBES
Within the framework of complex supergeometry and motivated by two-dimensional genus-zero holomorphic N = 2 superconformal field theory, we define the moduli space of N = 2 super-Riemann spheres with
The Notion of Vertex Operator Coalgebra and a Geometric Interpretation
The notion of vertex operator coalgebra is presented and motivated via the geometry of conformal field theory. Specifically, we describe the category of geometric vertex operator coalgebras, whose
Axiomatic Aspects of N = 2 Vertex Superalgebras with Odd Formal Variables
We formulate the notion of “N = 2 vertex superalgebra with two odd formal variables” using a Jacobi identity with odd formal variables in which an N = 2 superconformal shift is incorporated into the
On axiomatic aspects of N=2 vertex superalgebras with odd formal variables, and deformations of N=1 vertex superalgebras
The notion of "N = 2 vertex superalgebra with two odd formal variables" is presented, the main axiom being a Jacobi identity with odd formal variables in which an N=2 superconformal shift is
Linear automorphisms of vertex operator algebras associated with formal changes of variable and Bernoulli-type numbers
We study a certain linear automorphism of a vertex operator algebra induced by the formal change of variable $f(x)=e^x-1$ and describe examples showing how this relates the theory of vertex operator
VERTEX OPERATOR ALGEBRAS AND INTEGRABLE SYSTEMS
• Mathematics
• 2009
OF THE THESIS Vertex operator algebras and integrable systems by Shr-Jing Chen Thesis Director: Sergei Lukyanov and Yi-Zhi Huang The goal of this thesis is to explicitly construct vertex operator
The Notion of N=1 Supergeometric Vertex Operator Superalgebra and the Isomorphism Theorem
We introduce the notion of N=1supergeometric vertex operator superalgebra motivated by the geometry underlying genus-zero, two-dimensional, holomorphic N=1 superconformal field theory. We then show,

## References

SHOWING 1-8 OF 8 REFERENCES
A supergeometric interpretation of vertex operator superalgebras
Conformal field theory (or more specifically, string theory) and related theories (cf. [BPZ], [FS], [V], and [S]) are the most promising attempts at developing a physical theory that combines all
Two-Dimensional Conformal Geometry and Vertex Operator Algebras
The focus of this volume is to formulate and prove one main theorem, the equivalance between the algebraic and geometric formulations of the notion of vertex operator algebra. The author introduces a
Geometric interpretation of vertex operator algebras.
• Y. Z. Huang
• Mathematics
Proceedings of the National Academy of Sciences of the United States of America
• 1991
In this paper, Vafa's approach to the formulation of conformal field theories is combined with the formal calculus developed in Frenkel, Lepowsky, and Meurman's work on the vertex operator
148
• Birkhäuser, Boston,
• 1997
Free Lie Algebras, London Math. Soc. Monographs, New Series
• Free Lie Algebras, London Math. Soc. Monographs, New Series
• 1993
Application 4.10 The Neveu-Schwarz algebras for N > 1. For Grassmann envelopes of other superextensions of the Virasoro algebra
• Application 4.10 The Neveu-Schwarz algebras for N > 1. For Grassmann envelopes of other superextensions of the Virasoro algebra