Graded contractions of Virasoro algebras

TL;DR

This paper explores graded contractions of the Virasoro algebra, constructs highest weight representations, analyzes their reducibility, and discovers an exotic module with unique properties.

Contribution

It introduces new graded contractions of Virasoro algebra and identifies a novel exotic module with a null-plane at the fifth level.

Findings

Contracted representations are generally reducible.

Standard representations differ from contracted ones in reducibility.

An exotic module with a null-plane on the fifth level is found.

Abstract

We describe graded contractions of Virasoro algebra. The highest weight representations of Virasoro algebra are constructed. The reducibility of representations is analysed. In contrast to standart representations the contracted ones are reducible except some special cases. Moreover we find an exotic module with null-plane on fifth level.