Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The product on $\W$-spaces of rational forms

A. Zuevsky

Abstract

Let $V$ be a quasi-conformal grading-restricted vertex algebra, $W$ be its module, and $\W_{z_1, \ldots, z_n}$ be the space of rational differential forms with complex parameters $(z_1, \ldots, z_n)$ for $n \ge 0$. Using geometric interpretation in terms of two Riemann spheres sewing we define a product of elements of two spaces $\W_{x_1, \ldots, x_k}$ and $\W_{y_1, \ldots, y_n}$, and study its properties. A product is introduced also for elements of two spaces $C^k_m(V, \W)$ $\times$ $C^n_{m'}(V, \W)$ $\to$ $C^{k+n}_{m+m'}(V, \W)$ of the corresponding chain complex of rational differential forms invariant with respect to transformations of complex parameters.

The product on $\W$-spaces of rational forms

Abstract

Let be a quasi-conformal grading-restricted vertex algebra, be its module, and be the space of rational differential forms with complex parameters for . Using geometric interpretation in terms of two Riemann spheres sewing we define a product of elements of two spaces and , and study its properties. A product is introduced also for elements of two spaces of the corresponding chain complex of rational differential forms invariant with respect to transformations of complex parameters.

Paper Structure

This paper contains 26 sections, 26 theorems, 235 equations.

Table of Contents

  1. Conflict of Interest
  2. Data availability statement
  3. Introduction
  4. Spaces of $\mathcal{W}$-valued rational forms
  5. The space $\mathcal{W}$ of rational forms
  6. Properties of rational functions for $\mathcal{W}$-valued elements
  7. Product of spaces of $\mathcal{W}$-valued forms
  8. Motivation and geometric interpretation
  9. Definition of the product for $\mathcal{W}$-valued rational forms
  10. Existence of the corresponding rational form for the $\epsilon$-product
  11. Properties of the $\mathcal{W}$-product
  12. Spaces $C^n_m(V, \mathcal{W})$ of a complex
  13. $E$-elements
  14. Maps composable with vertex operators
  15. Definition of $C^n_m(V, \mathcal{W})$-spaces
  16. ...and 11 more sections

Key Result

Proposition 1

For primary vectors of a quasi-conformal grading-restricted vertex algebra $V$, the form bomba is invariant with respect to elements of the group ${\rm Aut}_{z_1, \ldots, z_n}\mathcal{O}^{(n)}$, i.e., under the changes of formal parameters $(z_1, \dots, z_n)$.

Theorems & Definitions (64)

  • Definition 1
  • Definition 2
  • Proposition 1
  • Definition 3
  • Proposition 2
  • Definition 4
  • Proposition 3
  • Definition 5
  • Remark 1
  • Proposition 4
  • ...and 54 more