$N$-point Virasoro Algebras and Their Modules of Densities

TL;DR

This paper introduces and analyzes n-point Virasoro algebras, generalizing classical Virasoro algebra, and constructs modules of densities with conditions for irreducibility, expanding understanding of their structure and representations.

Contribution

It defines n-point Virasoro algebras, explores their automorphisms, derivations, central extensions, and constructs modules of densities with irreducibility criteria.

Findings

Automorphism groups include C_n, D_n, A_4, S_4, A_5

Conditions for isomorphism of Lie algebras established

Criteria for irreducibility of modules of densities determined

Abstract

In this paper we introduce and study $n$-point Virasoro algebras, $\tilde{\W_a}$, which are natural generalizations of the classical Virasoro algebra and have as quotients multipoint genus zero Krichever-Novikov type algebras. We determine necessary and sufficient conditions for the latter two such Lie algebras to be isomorphic. Moreover we determine their automorphisms, their derivation algebras, their universal central extensions, and some other properties. The list of automorphism groups that occur is $C_n$, $D_n$, $A_4$, $S_4$ and $A_5$. We also construct a large class of modules which we call modules of densities, and determine necessary and sufficient conditions for them to be irreducible.