Basic equivariant gerbes on non-simply connected compact simple Lie groups

TL;DR

This paper investigates the existence of equivariant extensions of basic gerbes over non-simply connected compact simple Lie groups, providing explicit constructions and identifying obstructions.

Contribution

It computes obstructions and constructs basic equivariant bundle gerbes on non-simply connected compact simple Lie groups using modified methods.

Findings

Identified obstructions to equivariant gerbe extensions.

Constructed explicit basic equivariant bundle gerbes.

Extended previous methods to non-simply connected groups.

Abstract

This paper computes the obstruction to the existence of equivariant extensions of basic gerbes over non-simply connected compact simple Lie groups. By modifying a (finite dimensional) construction of Gaw\c{e}dzki-Reis [J. Geom. Phys. 50(1):28-55, 2004], we exhibit basic equivariant bundle gerbes over non-simply connected compact simple Lie groups.