Cohomology of the extended Schr\"odinger-Virasoro conformal algebra

TL;DR

This paper computes the cohomology groups of the extended Schr"odinger-Virasoro conformal algebra with trivial coefficients, introducing a new concept of relative cohomology to streamline results.

Contribution

It introduces the notion of relative cohomology for Lie conformal algebras and completely determines the cohomology groups of the algebra.

Findings

All basic cohomology groups are explicitly calculated.

Reduced cohomology groups are fully characterized.

Introduction of the relative cohomology concept simplifies the analysis.

Abstract

All the basic cohomology groups and reduced cohomology groups of the extended Schr\"odinger-Virasoro conformal algebra with trivial coefficients are completely determined. In particular, we introduce the notion of the relative cohomology of Lie conformal algebra, and then we can express our main results in a more concise manner.