Conformal operads and the basic vertex algebra cohomology complex

TL;DR

This paper introduces conformal pseudo operads and applies them to construct the basic cohomology complex of vertex algebras, building on Tamarkin's foundational ideas.

Contribution

It develops the concept of conformal pseudo operads and uses them to formulate the vertex algebra cohomology complex, advancing the algebraic understanding of vertex algebras.

Findings

Defined conformal pseudo operads for vertex algebra applications

Constructed the basic cohomology complex using these operads

Extended Tamarkin's work to a new algebraic framework

Abstract

We develop the notion of a (pro-) conformal pseudo operad and apply it to the construction of the basic cohomology complex of a vertex algebra. The paper heavily uses the ideas and constructions of the work of Tamarkin [Tam02]